Evans netted five goals in 96 appearances for West Brom. He joined them in 2015 from EPL heavyweights Manchester United, the BBC reported.
The Northern Ireland centre-back completed a medical at the King Power Stadium on Thursday.
West Brom dropped to the Championship at the end of this season and Evans had a clause in his contract which Leicester triggered after the relegation.
"It's great to join and I'm happy it's all gone through. 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," Evans was quoted as saying by the Guardian on Friday.
"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," he added.
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