"My reaction is that I am very happy to be at West Ham," the forward says in a statement released on the club's official website.
Zarate, who was the top scorer in the Argentine league last season, spent the second half of the 2007/08 Premier League campaign on loan at Birmingham from Qatari side Al Sadd. He then moved to Italian side Lazio and also played in Serie A for Inter Milan.
West Ham manager Sam Allardyce has been told to make his team more entertaining next season after securing a third straight year in the Premier League.