The centre-back’s Manchester City contract is due to expire at the end of June and he will officially join the Baggies after that.
Lescott had been a target for Stoke City and Hull City but has now agreed a two-year contract with West Brom, who recently named Alan Irvine as their new manager.
The England international played for the Baggies’ fierce rivals Wolverhampton Wanderers between 2000 and 2006 before a move to Everton, where Irvine had a coaching role at the time.
"I'm delighted we've been able to agree a deal with Joleon," said Irvine. "He's an England international and a proven Premier League player, who has been at the top level for a number of years.
"He's got Premier League and cup medals to his name and has had a fantastic career so far.
"When we realised he was available and there was a realistic chance of getting him here we started to work very hard on it.
"Full credit to the board and everyone at the club for getting this done as quickly and effectively as they did.
"I know Joleon and the type of personality and character he is, in addition to knowing what he can do as a player.
"He's a great professional and he will add to a number of very good professionals who are already in the squad."
Lescott, 31, has made 538 career appearances and scored 39 goals.
Good luck Joleon - A great defender who will be a massive asset to WBA. @dannyjohnson...Are you the captain of a Sports Journalism quiz team?- bernsteinforpm