OM confirmed the 28-year-old, who has been at the Ligue 1 club since 2011, made the switch to the Hawthorns in an early transfer deadline day move.
Amalfitano has one international cap for France and has also played for Lorient and Sedan.
Marseille confirmed in a statement on their official website: "Olympique de Marseille announce the loan with a purchase option for a permanent transfer for Morgan Amalfitano to English club West Bromwich Albion."
West Brom boss Steve Clarke is also looking to strengthen up front after seeing his side go a third straight league game without scoring.
Clarke's men are bottom of the table with just one point and he is hoping to have new resources available by the close of play.
"I've spoken at length about the need to bring fresh faces in to the club,'' he said.
"I hope there will be some good news for the supporters, we all need good news...even I need some good news.
"I need some players in forward areas that can give us a bit of quality so we create chances.
"All the top teams have that through the centre and have pace on the wider areas.