The 18-year-old, who can also play in midfield, handed in a transfer request last month amid reported interest from several Premier League clubs and has now got his wish after signing a five-year contract at Goodison Park.
Galloway became the youngest player to play for League One club MK Dons when he faced Nantwich Town at the age of 15 back in November 2011 and went on to make 17 appearances for the club.
And the teenager is determined to make the most of the opportunity to join Everton.
"It means an awful lot to me coming to such a great club," he told Everton'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."
