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.
Find all the latest football transfers on our dedicated page.
West Ham have signed Fenerbahce striker Emmanuel Emenike on loan, with an option to make the deal permanent at the end of the season.