The 27-year-old moves to the Boleyn Ground on a three-year contract for a fee believed to be in the region of £6 million.
Zarate moves to the club from Velez Sarsfield after scoring 13 goals in 19 league appearances and 20 in 35 in all competitions last season.
This will be the strikers’ second spell in England and the Premier League having previously played for Birmingham City when they were owned by current Hammers owners David Gold and David Sullivan. He scored 4 goals in 14 Premier League games for the Blues.