Martin Reilly - who represents the Northern Irishman - said that after four years and three title wins, the former club captain had decided he wanted to take on a fresh challenge.
He told Press Association Sport: "Four years is a good spell to be manager of a club like Celtic but now Neil wants to look ahead to the next chapter of his career."
BBC Scotland quoted Lennon as saying: "I have parted company with Celtic. I can't thank Peter Lawwell and the board enough for their backing and support.
"The club are in a very strong position and I wish the fans and the club all the very best for the future."
The 42-year-old replaced Tony Mowbray in 2010 and as well as leading the club to three successive Scottish Premiership successes, he has also helped the Hoops claim two Scottish Cup wins and masterminded their run to the last 16 of last season's Champions League.
That European campaign also included the famous Parkhead win over Barcelona and former Leicester midfielder Lennon is now expected to continue his career in England.
But despite being linked with the vacant managerial positions at Norwich and West Brom, Reilly insists his client has not agreed to any job offer yet.
He added: "He has nothing lined up. He just feels now is the time to move on to the next challenge."
Lennon originally signed as a player for the Glasgow giants in 2000 during Martin O'Neill's reign as Parkhead boss.
He won five titles in seven seasons and helped the club reach the 2003 UEFA Cup Final.
He left the club in 2007 to join Nottingham Forest but was later tempted back to Celtic Park a year later when Gordon Strachan offered him a role on the Hoops' coaching staff.
But after Mowbray's disastrous reign ended following a 4-0 humiliation away to St Mirren in March 2010, Lennon was given the top job.
He suffered an embarrassing Scottish Cup semi-final defeat to Ross County just three games into his stint in charge and was pipped to the Scottish title by Rangers a year later after his first full season in charge.
But at the end of that season, he told the Parkhead crowd: "This is not the end, it's just the beginning."
He stayed true to his word as he became only the fourth Celtic boss to lead the club to three titles in a row, joining Willie Maley, Jock Stein and Strachan in an exclusive club, as he made the most of Rangers' demotion to the bottom tier of the Scottish game.
However, controversy has never strayed far from Lennon during his time in Scotland.
He was given a four-match touchline ban following a spat with then Ibrox assistant manager Ally McCoist back in March 2011.
That same month, a parcel bomb addressed to the Celtic boss was intercepted by Royal Mail staff, while he was attacked in the dug-out at Tynecastle in May of that year after a supporter leapt from the Hearts end and charged straight for him.
Despite those ugly incidents, Reilly insisted Lennon had enjoyed his time in Glasgow's east end.
"It's been a fantastic journey for Neil since at Celtic," he said.
"He's enjoyed his time as a player, coach and now manager of the club and it's been fantastic for him.
"He has had good backing from the board and believes Celtic is a fantastic club, one of the biggest in the world. He wishes the club and the board all the very best for the future."
Meanwhile, bookmakers have already instilled former Celtic hero Henrik Larsson - currently in charge of Swedish outfit Falkenbergs - as the 1/3 favourite to replace Lennon as Hoops boss.
Please Vote - NUFC Player Of The Season
The voting runs until June 9th.
http://www.newcastleunited-mad.co.uk/interactive/voting_polls.asp
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World Cup Fixtures
Thursday 12th June 2014
21:00 Brazil Vs Croatia
Friday 13th June 2014
17:00 Mexico Vs Cameroon
20:00 Spain Vs Netherlands
23:00 Chile Vs Australia
Saturday 14th June 2014
17:00 Colombia Vs Greece
20:00 Uruguay Vs Costa Rica
23:00 England Vs Italy
Sunday 15th June 2014
02:00 Ivory Coast Vs Japan
17:00 Switzerland Vs Ecuador
20:00 France Vs Honduras
23:00 Argentina Vs Bos-Herce
Monday 16th June 2014
20:00 Iran Vs Nigeria
17:00 Germany Vs Portugal
23:00 Ghana Vs USA
Tuesday 17th June 2014
20:00 Brazil Vs Mexico
17:00 Belgium Vs Algeria
23:00 Russia Vs South Korea
Wednesday 18th June 2014
23:00 Cameroon Vs Croatia
17:00 Australia Vs Netherlands
20:00 Spain Vs Chile
Thursday 19th June 2014
17:00 Colombia Vs Ivory Coast
23:00 Japan Vs Greece
20:00 Uruguay Vs England
Friday 20th June 2014
17:00 Italy Vs Costa Rica
20:00 Switzerland Vs France
23:00 Honduras Vs Ecuador
Saturday 21st June 2014
17:00 Argentina Vs Iran
23:00 Nigeria Vs Bos-Herce
20:00 Germany Vs Ghana
Sunday 22nd June 2014
23:00 USA Vs Portugal
17:00 Belgium Vs Russia
20:00 South Korea Vs Algeria
Monday 23rd June 2014
21:00 Cameroon Vs Brazil
21:00 Croatia Vs Mexico
17:00 Australia Vs Spain
17:00 Netherlands Vs Chile
Tuesday 24th June 2014
21:00 Greece Vs Ivory Coast
21:00 Japan Vs Colombia
17:00 Costa Rica Vs England
17:00 Italy Vs Uruguay
Wednesday 25th June 2014
21:00 Ecuador Vs France
21:00 Honduras Vs Switzerland
17:00 Bos-Herce Vs Iran
17:00 Nigeria Vs Argentina
Thursday 26th June 2014
17:00 Portugal Vs Ghana
17:00 USA Vs Germany
21:00 Algeria Vs Russia
21:00 South Korea V Belgium
NEWCASTLE UNITED 2013/14
PREMIER LEAGUE
LIVERPOOL 2 NEWCASTLE 1 (Skrtel og)
Krul, Debuchy, S Taylor (73' de Jong), Williamson, Coloccini, Haidara, Sissoko, Anita, Tiote (82' Dummett), Gouffran (78' Sammy Ameobi), Shola Ameobi
Subs: Santon, Yanga-Mbiwa, Elliot, Satka
NEWCASTLE 3 CARDIFF CITY 0 (Shola Ameobi, Remy, S Taylor)
Krul, Debuchy, Williamson, Coloccini, Dummett (45' Haidara), Sissoko, Tiote, Anita (79' S Taylor), Gouffran (70' Gosling), Remy, Shola Ameobi
Subs: Yanga-Mbiwa, de Jong, Elliot, Armstrong
ARSENAL 3 NEWCASTLE 0
Krul, Debuchy (84' Yanga-Mbiwa), Williamson, Coloccini, Dummett, Tiote, Anita, Sissoko, Gosling (69' Shola Ameobi), Gouffran (89' Armstrong), Remy
Subs: Haidara, Elliot, Obertan, S Taylor
NEWCASTLE 1 SWANSEA 2 (Shola Ameobi)
Krul, Anita, Williamson, Coloccini, Dummett, Gosling (81' Armstrong), Tiote, Cisse (21' Debuchy), de Jong (40' Remy), Gouffran, Shola Ameobi
Subs: Yanga-Mbiwa, Haidara, Elliot, S Taylor
STOKE 1 NEWCASTLE 0
Krul, S Taylor (61' Yanga-Mbiwa), Williamson, Coloccini, Anita, Gosling (73' Gouffran), Tiote, Dummett, Cisse (74' Armstrong), Shola Ameobi
Subs: de Jong, Haidara, Bigirimana, Elliot
NEWCASTLE 0 MAN UTD 4
Elliot, Santon, Williamson, Coloccini, Haidara, Tiote, Gosling, Anita, de Jong (61' Ben Arfa), Gouffran (85' Shola Ameobi), Cisse
Subs: Yanga-Mbiwa, S Taylor, Dummett, Alnwick, Armstrong
SOUTHAMPTON 4 NEWCASTLE 0
Elliot, Yanga-Mbiwa (45' Santon), Williamson, Coloccini, Haidara, Anita, Tiote, Ben Arfa (45' de Jong), Sissoko (78' Dummett), Gouffran, Cisse
Subs: Gosling, Shola Ameobi, S Taylor, Alnwick
NEWCASTLE 0 EVERTON 3
Krul, Yanga-Mbiwa (75' Marveaux), Williamson, Coloccini, Dummett, Sissoko, Anita, Tiote, Gouffran (90+1' Shola Ameobi), de Jong (58' Ben Arfa), Cisse
Subs: Gosling, Haidara, Elliot, S Taylor
NEWCASTLE 1 CRYSTAL PALACE 0 (Cisse)
Krul, Yanga-Mbiwa, Williamson, Coloccini, Dummett, Sissoko (88' Marveaux), Tiote, Anita, Gouffran (76' Shola Ameobi), de Jong (59' Ben Arfa), Cisse.
Subs: Gosling, Haidara, Elliot, S Taylor.
FULHAM 1 NEWCASTLE 0
Krul, Yanga-Mbiwa, Williamson, Coloccini, Dummett, Sissoko, Tiote, Anita (81' Marveaux), Gouffran, de Jong (86' Armstrong), Cisse (71' Shola Ameobi).
Subs: Gosling, Haidara, S Taylor, Alnwick
HULL CITY 1 NEWCASTLE 4
Krul, Debuchy, Williamson, Yanga-Mbiwa, Dummett, Sissoko, Tiote, Anita, Gouffran, de Jong (90' Gosling), Remy
Subs: Cisse, Haidara, Marveaux, Shola Ameobi, S Taylor, Alnwick
NEWCASTLE 1 ASTON VILLA 0 (Remy)
Krul, Debuchy, Williamson, Coloccini, Dummett, Sissoko, Cheick Tiote (89' Gosling), Anita, Gouffran, Remy, Cisse (72' de Jong).
Subs: Yanga-Mbiwa, Haidara, Elliot, Shola Ameobi, S Taylor
NEWCASTLE 0 SPURS 4
Krul, Debuchy, Williamson, S Taylor, Santon (45' Dummett), Anita, Sissoko, Gouffran, de Jong (63' Ben Arfa), Sammy Ameobi (71' Marveaux), Cisse
Subs: Yanga-Mbiwa, Gosling, Elliot, Shola Ameobi
CHELSEA 3 NEWCASTLE 0
Krul, Debuchy (40' Yanga-Mbiwa), Williamson, S Taylor, Dummett, Anita (84' Marveaux), Santon, Ben Arfa (64' Gosling), Sissoko, Sammy Ameobi, de Jong.
Subs: Haidara, Elliot, Shola Ameobi, Armstrong
NEWCASTLE 0 SUNDERLAND 3
Krul, Debuchy, Williamson, S Taylor, Santon (64' Dummett), Anita (74' Marveaux), Tiote, Sissoko, Ben Arfa, Sammy Ameobi (45' de Jong), Shola Ameobi.
Subs: Yanga-Mbiwa, Haidara, Elliot, Armstrong
NORWICH 0 NEWCASTLE 0
Krul, Debuchy, Williamson, S Taylor, Santon, Anita, Tiote, Ben Arfa (75' Shola Ameobi), Sissoko, Sammy Ameobi (87' Haidara), Remy
Subs: Yanga-Mbiwa, Gosling, Elliot, Dummett, Armstrong
WEST HAM 1 NEWCASTLE 3 (Cabaye 2, Remy)
Krul, Yanga-Mbiwa, Williamson, S Taylor, Santon (74' Dummett), Tiote, Anita (60' Shola Ameobi), Sissoko, Cabaye, Gouffran, Remy (78' Ben Arfa)
Subs: Cisse, Haidara, Elliot, Obertan
NEWCASTLE 0 MAN CITY 2
Krul, Yanga-Mbiwa (82' Ben Arfa), Williamson, S Taylor, Santon, Anita (73' Cisse), Tiote, Sissoko, Cabaye, Gouffran (82' Haidara), Remy
Subs: Gosling, Elliot, Marveaux, Sammy Ameobi
WEST BROM 1 NEWCASTLE 0
Krul, Debuchy, Williamson, Coloccini (65' Yanga-Mbiwa), Santon, Cabaye, Tiote, Gouffran (45' Ben Arfa), Sissoko, Remy, Shola Ameobi (76' Haidara).
Subs: Anita, Cisse, Elliot, S Taylor
NEWCASTLE 0 ARSENAL 1
Krul, Debuchy, Williamson, Coloccini, Santon, Anita (74' Shola Ameobi), Tiote, Sissoko (79' Haidara), Cabaye, Gouffran (62' Ben Arfa), Remy
Subs: Cisse, Yanga-Mbiwa, Elliot, Sammy Ameobi
NEWCASTLE 5 STOKE CITY 1 (Remy 2, Gouffran, Cabaye, Cisse pen)
Krul, Debuchy, Williamson, Coloccini, Santon (61' Haidara), Anita (45' Shola Ameobi), Sissoko, Ben Arfa, Cabaye, Gouffran (72' Cisse), Remy
Subs: Yanga-Mbiwa, Elliot, Obertan, S Taylor
CRYSTAL PALACE 0 NEWCASTLE 3 (Cabaye, Gabbidon og, Ben Arfa pen)
Krul, Debuchy, Williamson, Coloccini, Santon, Anita, Tiote, Sissoko, Cabaye (79' Ben Arfa), Gouffran, Remy (75' Shola Ameobi).
Subs: Cisse, Yanga-Mbiwa, Haidara, Elliot, Obertan
NEWCASTLE 1 SOUTHAMPTON 1 (Gouffran)
Krul, Debuchy, Williamson, Coloccini, Santon (78' Haidara), Sissoko, Anita, Tiote, Gouffran (73' Ben Arfa), Shola Ameobi (61' Cisse), Remy
Subs: Yanga-Mbiwa, Elliot, Obertan, Sammy Ameobi
MAN UTD 0 NEWCASTLE 1 (Cabaye)
Krul, Debuchy (83' Yanga-Mbiwa), Williamson, Coloccini, Santon, Cabaye (78' Shola Ameobi), Tiote, Anita, Sissoko, Remy, Gouffran (57' Ben Arfa).
Subs: Cisse, Gutierrez, Elliot, Obertan
SWANSEA 3 NEWCASTLE 0
Krul, Debuchy, Williamson (77' Yanga-Mbiwa), Coloccini, Santon (56' Haidara), Sissoko, Tiote, Cabaye, Gouffran, Shola Ameobi (67' Obertan), Remy
Subs: Anita, Elliot, Sammy Ameobi, Dummett
NEWCASTLE 2 WBA 1 (Gouffran, Sissoko)
Krul, Debuchy, Williamson, Coloccini, Santon, Sissoko (90+5' Cisse), Tiote, Cabaye, Gouffran, Shola Ameobi, Remy (84' Anita)
Subs: Ben Arfa, Yanga-Mbiwa, Elliot, Obertan, Sammy Ameobi
NEWCASTLE 2 NORWICH CITY 1 (Remy, Gouffran)
Krul, Yanga-Mbiwa, Williamson, Coloccini, Santon, Sissoko, Tiote, Cabaye (68' Anita), Gouffran (83' Ben Arfa), Shola Ameobi (74' Cisse), Remy.
Subs: Haidara, Elliot, Obertan, Sammy Ameobi
TOTTENHAM 0 NEWCASTLE UTD 1 (Remy)
Krul, Debuchy, Williamson, Yanga-Mbiwa, Santon, Sissoko, Cabaye, Tiote, Gouffran (85' Obertan), Remy (75' Cisse), Shola Ameobi (60' Anita).
Subs: Coloccini, Ben Arfa, Elliot, Sammy Ameobi
NEWCASTLE UTD 2 CHELSEA 0 (Gouffran, Remy)
Krul, Debuchy, Williamson, Yanga-Mbiwa, Santon, Sissoko, Cabaye, Tiote (53' Anita), Gouffran (85' Obertan), Shola Ameobi (62' Cisse).
Subs: Ben Arfa, Elliot, Sammy Ameobi, Tavernier.
SUNDERLAND 2 NEWCASTLE 1 (Debuchy)
Krul, Debuchy, Williamson, Dummett, Santon, Sissoko (45' Cisse), Tiote, Cabaye, Gouffran (86' Sammy Ameobi), Ben Arfa, Remy (70' Shola Ameobi).
Subs: Anita, Haidara, Elliot, Obertan.
NEWCASTLE UTD 2 LIVERPOOL 2 (Cabaye, Dummett)
Krul, Debuchy, Williamson, Yanga-Mbiwa, Santon, Cabaye (78' Sammy Ameobi), Tiote, Gouffran, Sissoko (45' Dummett), Remy, Ben Arfa (78' Anita).
Subs: Cisse, Elliot, Obertan, Dummett.
CARDIFF CITY 1 NEWCASTLE 2 (Remy 2)
Krul, Debuchy, Williamson, Coloccini, Santon, Tiote, Cabaye (86' Ben Arfa), Gouffran, Sissoko, Remy (71' Gutierrez), Cisse
Subs: Anita, Yanga-Mbiwa, Elliot, Sammy Ameobi, Dummett
EVERTON 3 NEWCASTLE 2 (Cabaye, Remy)
Krul, Debuchy, Yanga-Mbiwa (46' Williamson), Coloccini, Santon, Tiote, Anita (69' Cisse), Ben Arfa (46' Cabaye), Sissoko, Gouffran, Remy
Subs: Elliot, Obertan, Sammy Ameobi, Dummett
NEWCASTLE 2 HULL CITY 3 (Remy 2)
Krul, Debuchy (86' Tiote), Yanga-Mbiwa, Coloccini, Santon, Cabaye (62' Gouffran), Anita, Sissoko, Ben Arfa, Cisse (73' Marveaux), Remy
Subs: Williamson, Elliot, Sammy Ameobi, Dummett
ASTON VILLA 1 NEWCASTLE 2 (Ben Arfra, Gouffran)
Krul, Debuchy, Coloccini, Yanga-Mbiwa, Santon, Anita (74' Tiote), Cabaye (88' Sammy Ameobi), Ben Arfa, Sissoko, Remy (63' Gouffran), Cisse
Subs: Elliot, Marveaux, S Taylor, Dummett
NEWCASTLE 1 FULHAM 0 (Ben Arfa)
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita 65' (Cabaye), Marveaux 74' (Remy), Shola Ameobi 65' (Gouffran), Cisse
Subs: Gosling, Elliot, Sammy Ameobi, Dummett
NEWCASTLE 0 WEST HAM 0
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita, Marveaux 66' (Sammy Ameobi), Shola Ameobi, Cisse 72'
Subs: Gosling, Bigirimana, Elliot, Vuckic, Dummett
MAN CITY 4 NEWCASTLE 0
Krul, Debuchy, Coloccini, S Taylor, Yanga-Mbiwa, Sissoko, Tiote, Gouffran 45+4' (Dummett), Ben Arfa 65' (Sammy Ameobi), Gutierrez 44' (Anita), Cisse
Subs: Elliot, Marveaux, Shola Ameobi, Obertan
LEAGUE CUP
NEWCASTLE 0 MAN CITY 2 (AET)
Krul, Debuchy, Williamson, Yanga-Mbiwa, Haidara (45 Dummett, 80 Ben Arfa), Anita, Tiote, Gouffran, Sissoko, Shola Ameobi (66 Cabaye), Cisse
Subs: Remy, Elliot, Obertan, Sammy Ameobi
NEWCASTLE 2 LEEDS UTD 0 (Cisse, Gouffran)
Krul, Debuchy, Williamson, Coloccini, Dummett, Gouffran (90' Vuckic), Anita (80' Gosling), Tiote, Marveaux, Sammy Ameobi, Cisse (71' Obertan).
Subs: Ben Arfa, Yanga-Mbiwa, Bigirimana, Alnwick
MORECAMBE 0 NEWCASTLE 2 (Shola Ameobi, Sammy Ameobi)
Elliot, Debuchy, Yanga-Mbiwa, Good, Dummett, Bigirimana, Gosling, Marveaux 88' (Sissoko), Vuckic 46' (Shola Ameobi), Sammy Ameobi, Gouffran 71' (Ben Arfa)
Subs: Santon, Anita, Alnwick, Streete
FA CUP
NEWCASTLE 1 CARDIFF CITY 2 (Cisse)
Elliot, Santon, S Taylor, Yanga-Mbiwa, Haidara, Sissoko (85' Shola Ameobi), Tiote, Anita, Gouffran (63' Obertan), Ben Arfa, Cisse (85' Remy).
Subs: Williamson, Sammy Ameobi, Dummett, Alnwick