The Wigan-born 18-year-old, who had been with the Reds at the age of eight, is an energetic midfielder with an eye for goal and will initially be part of United's under-23s squad.
He has also played at centre-back earlier in his career and made his under-18s bow for Liverpool as a 15-year-old under Steven Gerrard in 2017/18.
Brookwell turned down offers from other Premier League clubs, as well as elsewhere in the Football League, to join the Magpies.
Chris Hogg, Newcastle United's lead player development coach for the club’s under-23 side, told nufc.co.uk: "He's got good pedigree, having come through the Liverpool Academy - he's worked with a lot of good people there and has some good habits and a real good work ethic.
"I'd watched a lot of his clips before we signed him, and having seen him in the flesh in training he seems to be a good character, a good personality to have in the building, and somebody who we're hoping we can add a few more layers to, in terms of his football and personally, where he can be a success at the football club."
Photograph courtesy of Nick Taylor, Liverpool FC