The 19-year-old has signed a four-and-a-half-year contract with the Premier League side.
Nsereko will join the Hammers for a fee believed to be around £9million.
West Ham chief executive Scott Duxbury said: “We are delighted to sign Savio, particularly with the fierce competition for his services across Europe.
“He is an exciting prospect, who Gianfranco Zola believes will prove a valuable asset for this club now and in the years to come.
“It is a significant investment and shows our determination to continue moving this club forward.”
