The Baggies have completed a move for the versatile 28-year-old attacking midfielder, who has won one cap for France but became surplus to requirements at the Stade Velodrome
Amalfitano can play centrally or out wide and was awarded one international cap for France in 2012 after joining Marseille in 2011 from Lorient.
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“I’m delighted to welcome Morgan to the club," Clarke told West Brom's official website.
“He is predominantly a right-sided midfielder who can also operate in a number of other midfield and attacking positions.
"Morgan is a technical player with good quality on the ball. He also has fantastic work-rate and we believe his game is well suited to the Barclays Premier League.
"Morgan’s arrival will increase competition in midfield and add more quality and depth to the squad."