In a frantic deadline-day move, Amalfitano joined West Ham from Ligue 1 outfit Marseille on a one-year deal for an undisclosed fee.
Amalfitano, who scored four goals during his season-long loan spell with Premier League rivals West Brom in 2013-14, was desperate to end his three-year stay in Marseille following a reported bust-up with coach Marcelo Bielsa last month.
"It's very good news and I'm very happy to come to this big club," Amalfitano told West Ham's official website.
"I've waited a long time, but I am very happy to have signed here. The club wanted me a lot and for that I waited for West Ham and now I'm here."
Amalfitano added: "I enjoyed my first year in English football and for that reason I have come back and hopefully I can improve again.
"The first year was good for my experience and I will try to help West Ham now by giving my best and continue to improve in this league. I like this country and this is the best league."
Amalfitano is Sam Allardyce's ninth recruit following the arrivals of Mauro Zarate, Cheikhou Kouyate, Aaron Cresswell, Diego Poyet, Enner Valencia, Carl Jenkinson (loan), Diafra Sakho and Alex Song (loan).
