The Wigan left-back yesterday joined his boyhood club in a £5million deal, which could rise to £6m.
But Baines, 22, would have picked up a bigger wage packet had he moved to St James' Park.
He said: "I'd like to thank all the staff at Wigan.
"I've had six fantastic years here and it was a really tough decision to leave that behind. This is the club who have given me the opportunity to make it in the game.
"It's been a real adventure here and it's one I'll never forget but I need a fresh challenge.
"I think the team will do well under Chris Hutchings and I'm sure the supporters will get the success they deserve."
Assistant boss Alan Irvine reckons Everton have landed a future England international in Baines.
He insisted: "Leighton has real potential to play for his country. Anyone who saw him in the European Under-21 Championships would have been impressed with him.
"He is a good footballer, a nice passer of the ball and has loads of energy. He's also quick so there are lots of reasons for wanting to sign a player like him."