The veteran midfielder was at the Baggies' training ground on Tuesday to undergo a medical ahead of a £1m move.
The England international has slipped down the pecking order at Goodison Park in the last 12 months following the arrivals of the likes of Morgan Schneiderlin, Idrissa Gueye and Davy Klaassen and the emergence of Tom Davies and he is believed to be keen to play more regular football as he enters the twilight years of his career.
The 35-year-old made 23 Premier League stars for the 'Toffees' last season and West Brom boss Tony Pulis sees the experienced midifelder as the ideal replacement for Darren Fletcher, who joined Stoke earlier this summer.
The former Manchester City man needs to make just five more Premier League appearances in order to beat Ryan Giggs' all-time record of 632.
There are not expected to be any late hitches and the deal should be tied up in the next 24 hours or so.