"It's great to join and I'm happy it's all gone through", Evans told LCFC TV.
Arsenal and City were most heavily linked, while Leicester joined the race for his signature back in January.
Three-time Premier League champion Evans said: "When this opportunity came up, it's one that I couldn't turn down".
"I hope that I can give lots to the team and the club".
And the former Manchester United defender has hailed Leicester's ambitious owners as a key factor in his decision to sign.
However, Leicester have been in talks with Evans' representatives for several weeks and were always confident of completing a deal.
Northern Ireland worldwide Evans is Leicester's second signing in the close season after Portuguese defender Ricardo Pereira's arrival last month.
Leicester boss Claude Puel will overhaul his defence this summer with Robert Huth set to be released when his contract expires and title-winning skipper Wes Morgan, 34, expected to play a reduced role.
Tomas Kalas, Chelsea- The Czech Republic worldwide has spent the last two season on loan at Fulham in the Championship from Chelsea.
Everton and Fulham are also said to be interested in the England under-21 global but Maddison is believed to prefer a move to Leicester to be closer to his family.