The centre-back joins the Foxes on a three-year deal after the Foxes agreed to pay the former Manchester United defender's relegation release clause.
Northern Ireland international Evans had attracted interest from Arsenal and Manchester City during the January transfer window, but the Baggies were able to hold on to him for the remainder of the campaign.
Instead, it is the Foxes who have snapped him up after West Brom dropped to the Championship.
“It’s great to join and I’m happy it’s all gone through," Evans told the club's website. "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 club."
Leicester boss Claude Puel said of the former Manchester United star: "Jonny is a player of great experience in the Premier League and to have him as part of our squad is fantastic news for the football club.
"He knows exactly what it takes, he is a winner and a leader. He will bring a great deal to our squad and I’m delighted to welcome him to Leicester City."
Evans becomes Puel's second summer signing following the arrival of Ricardo Pereira from Porto and will provide competition for Harry Maguire and Wes Morgan following the decision to release veteran Robert Huth.