Striker Armstrong and goalkeeper Woodman are both 17, whilst Slovakian defender Satka is 18.
England youth star Armstrong has already made his Premier League debut, whilst Satka has also been involved in the first-team in recent weeks.
Newcastle announced the deals whilst also confirmed their Academy has been awarded Category One status - the highest ranking under the Premier League's Elite Players Performance Plan (EPPP).
"Being a Category One Academy is extremely important in terms of looking to the future and giving young talented players the best possible chance of succeeding at Newcastle United," said Pardew.
"I know our supporters love to see young players like Sammy Ameobi and Paul Dummett come through, and that's why I'm pleased to see Adam, Freddie and Lubo sign their first professional contracts.
"This is only a first step on the career ladder for these boys and they must continue to show the same commitment and desire and will to learn as they have to this point."