The England international fell out of favour at the Etihad Stadium under Manuel Pellegrini and had been all but confirmed to leave the club.
He is the club's first signing since Alan Irvine's appointment as head coach on Saturday and will join on a two-year contract, with a further performance-related option for another year.
Irvine and Lescott worked together at Everton, where the Scot was assistant to David Moyes.
"I'm delighted we've been able to agree a deal with Joleon," Irvine told the club's official website.
"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."
With West Brom having signed Craig Gardner from Sunderland in the close-season, Lescott is the club's second acquisition since narrowly escaping relegation last term.
After a disastrous campaign that saw Steve Clarke, Keith Downing and Pepe Mel all take charge and West Brom finish 17th, technical director Terry Burton said their recruitment is a positive sign.
"Joleon is the second of two quality signings we have made so far this summer and we hope to continue in that vein," he added.
"Joleon and Craig will not only add quality to the squad but character as well, which is vitally important for the Premier League challenge."
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