The club announced the news on their official website, with Baker signing until the end of the season.
The reason the Dons need Baker is due to the injury to Tottenham-bound Dele Alli, who is at the Premier League side undergoing treatment at present.
He has scored 14 goals this season, and Baker, who netted 26 from midfield for Chelsea's youth side last season is seen as a like for like replacement to fill the void.
The duo already know each other from the England youth set up, and Alli sent a message of congratulations to both player and club upon the move being announced.
Baker had signed on loan earlier this year with Championship side Sheffield Wednesday, but played 90 minutes just once and Chelsea recalled him, keen to see him at a club where he will be playing regularly in order to benefit his development.
The 19-year-old has a chance to slot straight in and start living up to his potential, by replacing Alli. If he can help MK Dons gain promotion, there is a decent prospect that the club may attempt to try to persuade Chelsea to let them have him on loan in the Championship next season.