Schneiderlin, 27, has signed a four-and-a-half-year contract with the Merseyside outfit and will reunite with Everton boss Ronald Koeman, who managed the defensive midfielder for one season at Southampton.
"Everton is a big club in the history of English football. I've always loved the atmosphere in the stadium. I've always liked playing here. I can't wait to play and to represent this great club," Schneiderlin, who could make his Toffees debut against Manchester City on Sunday, told the club's official website.
"There is a manager in place here that I know, I know he can get the best out of me, I know his style and how he likes to play football. He was very good with me from the start and I enjoyed playing football under him. He was very good for me and, obviously, he was a massive player in his playing days and you can only learn from the best. At Southampton he gave me some great advice to keep improving every day and it was a pleasure to work with him.
"We spoke since the time I knew Everton would be interested. I know his ambition and why he came here. He believes in this and I do, too. We are trying to achieve something here and this is what I am here for. I know the fans have big expectations and we'll do everything to make them come true."
Koeman added: "I'm very pleased because I know the player, I know the qualities of the player, I know him as a person and he's really desperate to come to Everton - and that's what we need. We want good players but we also want players who really want to show their qualities in front of the fans of Everton.
"He's a strong character. I worked with him for one season at Southampton and he's a midfield player who can play in different positions in the midfield. He's also a fast player, he's a clever player and he's a personality. Normally, he's part of the French national team and at 27 years old he's part of the future at Everton.
"Morgan is really hungry to show his qualities and to play because that is the best thing for a football player. You are born as a football player to play games, not to sit on the bench or not be part of the team. But this is a new step, it's a new future and he will show his qualities. I am convinced of that."
Louis van Gaal brought Schneiderlin, who could end up costing Everton £24m, to Man United in the summer of 2015, but the midfielder has struggled for first-team action under Jose Mourinho this season - playing just 11 minutes of Premier League football during the 2016-17 campaign.