The former Birmingham City, Lazio and Inter Milan forward finished last season as the top scorer in Argentina's Primera Division with 13 goals.
Zarate's last spell in England saw him net four times in 14 games for Birmingham during a loan spell from Al Sadd in 2008.
When asked if he had agreed a three-year deal with the Hammers, the 27-year-old told Sky Sports News: "Yes. It's a new chance for me. West Ham called me. They are a fierce team and now I think I want to play [there]."