Amalfitano will provide further midfield cover for Clarke as he looks to build on last season's ninth-place finish in the Premier League.
The 28-year-old provided 30 assists in the past four seasons and will offer creative flair in the middle of the pitch for West Brom.
He becomes the fifth arrival at the Hawthorns since last term and Clarke believes that he will add a new dimension to his attacking options.
"I'm delighted to welcome Morgan to the club," the Scot told the club'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 Premier League.
"Morgan's arrival will increase competition in midfield and add more quality and depth to the squad."
The France international made 26 appearances in Ligue 1 last season, and has featured twice as a substitute in the current campaign.
