Fortune, 32, was available on a free transfer after seeing out his contract at the Hawthorns and has agreed a two-year deal.
Wigan boss Owen Coyle has been busy in the transfer market in the last few weeks; Fortune becomes his sixth summer signing.
Coyle said: "To bring a player of such calibre to the football club is a great piece of business.
"He's shown his qualities at the very highest level, and when I spoke to Steve Clarke at West Brom he told me how he didn't want to lose him, proof that he has the capabilities to be a Premier League forward, never mind a Championship one.
"He's powerful, can play anywhere across the front line and has pace to hurt defences. It's important to have these kind of players at the club."
The Frenchman scored two goals in 23 appearances for West Brom last season, but Coyle sees him as an ideal replacement for Everton and Newcastle target Arouna Kone.
In total he made 80 league appearances for the Baggies either side of a year with Celtic, whom he joined from French side Nancy.