The 29-year-old has fallen foul of Paolo Di Canio's close-season clearout at the Stadium Light and becomes West Brom's fifth signing of the current transfer window.
He has signed a three-year contract with Steve Clarke's side, who have also bolstered their attacking ranks with the signings of Morgan Amalfitano, Scott Sinclair, Matej Vydra and Nicolas Anelka of late.
Sessegnon first arrived in England in January 2011, as he completed a move from Paris Saint-Germain to Sunderland for a fee in the region on £6million.
He has since scored 17 goals in 87 Premier League appearances, but has been deemed surplus to requirements by Di Canio.
Sessegnon represents Benin at international level and has been a regular fixture for his national team since making his debut against Cameroon in 2004.
West Brom have made a poor start to the 2013-14 campaign and sit rock-bottom of the Premier League after earning just one point from their first three games.
