The 19-year-old, who is currently on duty with England's Under-20s, will link-up with his new team-mates after the international break and remain at Oakwell until January 3.
Armstrong spent last season on loan at Coventry where he recorded 20 goals from 40 appearances and claimed the Sky Blues' top scorer award.
A club statement from Barnsley read: "The Reds fought off a whole host of suitors for the prolific goal scoring talent and we are delighted to welcome him to Oakwell.
"The striker's stunning ability to finish has seen him score a complete range of goals from close-range finishes inside the area, to long distance strikes. He has the talent to use both feet when taking chances, as well as the ability to springboard off the floor to score headers."
Tykes head coach Paul Heckingbottom is looking forward to welcoming Armstrong to his ranks as he told his club's official website: "Firstly, I am very thankful to Newcastle United for allowing Adam to come on loan here. He is a player I am incredibly pleased to bring to the club and one I have been enquiring about for some time.
"His talent and goal scoring abilities are clear to see as he was excellent in League One last season scoring a ton of goals. We've started the season in great form, scoring a lot of goals and I have no doubts that Adam will make an instant impact and excite the fans."
Armstrong, who signed a new deal with the Magpies that will keep him at St. James' Park until 2020, has made two substitute appearances for Rafael Benitez's side this season but - under the terms of his loan - he will be ineligible to play when Newcastle face Barnsley at Oakwell on Tuesday, October 18.