According to various outlets, the Foxes have moved for the defender following the West Midlands' club's relegation from the Premier League and will pay the £3.5million escape clause in the defender's contract.
The move is expected to be complete by the end of the week after Evans, 30, held talks with Leicester boss Claude Puel and agreed personal terms on his switch to the King Power Stadium.
Long term target
The conclusion of the transfer would bring to an end a long, drawn-out saga for the former Manchester United man and Leicester themselves. The 2015-16 Premier League champions have been interested in acquiring his services for some time and reportedly had a £23million bid rejected in the summer transfer window.
Upon his arrival in the East Midlands, he will be competing with the likes of Harry Maguire, Wes Morgan, Yohan Benalouane and Daniel Amartey for the centre back berth. Robert Huth has already departed Leicester following the expiry of his contract.
Evans would become Leicester's second signing of the summer following the arrival of FC Porto defender Ricardo Pereira right at the start of the window.
It is clear to see why Puel has moved to bring in the defender. Having made 235 appearances in the Premier League, he has won three titles, as well as two League Cups with Manchester United. Evans also played a role as the Red Devils lifted the UEFA Champions League in 2008.
Since moving to the Hawthorns, he has made 96 appearances, including 28 last season as the Baggies slipped into the Championship.