Evans had attracted interest from a number of clubs, but he has joined Leicester for £3.5million after the 'Foxes' activated his relegation release clause.
"It's great to join and I'm happy it's all gone through," Evans told 'LCFC TV'.
"When this opportunity came up, it's one that I couldn't turn down. It's an ambitious club, the owners are ambitious and everyone wants to push the club forward.
"I hope that I can give lots to the team and the club. It's a great place to play football, the fans really get behind the team and the players are fantastic - these are all factors that made me want to sign for this football club."
Evans joins after a disappointing season that saw West Brom relegated, although the defender was subject to bids from Arsenal and Manchester City earlier in the season, proving that his stock had not fallen.
He joined West Brom after a successful spell with Manchester United, where Alex Ferguson brought him through the academy.