The former Chelsea frontman, who spent the second half of last season on loan to Juventus from Shanghai Shenhua, has signed a one-year deal with the Baggies.
"I know the club because I know the manager [Steve Clarke]," Anelka told the club's official YouTube channel. "He likes to play football and he wants to play football. I am 34 years old now and I want to enjoy my football. I think this is the right move for me."
West Brom is the sixth Premier League club that Anelka has played for.