The Nigeria international has been on loan at Qatari club Al Ain this season.
“I’m very happy and very excited that I’m here,” 28-year-old Emenike told the club’s website.
“I have always known West Ham as a great club. I have known [manager Slaven] Bilic for years and thank God we are here together.”
Bilic previously managed Besiktas, based in Istanbul, Turkey – the city rivals of Fenerbahce.
Emenike, who has scored nine goals in 37 international appearances, becomes the club’s second signing of the January transfer window, after Leeds defender Sam Byram.