The 18-year-old, who formally expressed his desire to leave the Football Club last month, has signed a five-year contract with the Goodison Park outfit after both clubs agreed a deal for the England Under-19 international.
Speaking to mkdons.com, Manager Karl Robinson added: “It’s disappointing for the Club and it’s disappointing for me to lose a player of Brendan’s quality.
“I do believe Brendan can be as good as he wants to be and I wish him all the luck in the world. He’s going to a fantastic football club in Everton that will only aid his development.
Robinson continued: “The two clubs have conducted themselves very well during the last month and there’s been constant dialogue all the time. The two clubs have always been looking to do the best thing possible for the player.”
Executive Director Andrew Cullen said: “Everyone at MK Dons is naturally disappointed that Brendan has chosen to continue his development elsewhere, but we understand the lure of the Premier League is enormous.
“Brendan is a very talented young player who we have no doubt will be a great success at Everton and at international level with England, and we all wish him every success with his future career.”