The 18-year-old centre-back has signed a five-year contract with Roberto Martinez's side and will initially join up with the club's Under-21 squad
Galloway, who has appeared for England at Under-19 level, has signed a five-year contract with Everton and will initially join up with the club’s Under-21s squad.
Galloway made his first-team debut for MK Dons at the age of 15 in 2011 and appeared 13 times for the League One side last season.
"It means an awful lot to me coming to such a great club," Galloway told the club’s official website.
"I'm now looking forward to learning off some of the more senior players - the likes of Sylvain Distin and Phil Jagielka.
"I've been watching them for years now and they're great professionals, great players - players who have been there and done it. That's a big thing for me to be able to learn off guys like that.
"Short-term, I just want to work hard to better myself as a footballer here, which I know I will with the coaches and other staff here.
"Long-term, I also want to get in the Everton team and play week in and week out in the Premier League and play in a team that's doing well, which I know we will do."