The Argentine forward agreed a three-year deal at Upton Park last week and wants to hit the ground running on his second spell in the Premier League.
Zarate played for Birmingham City on loan in the 2007-08 season and has since played in Italy and his homeland.
The 27-year-old will provide West Ham boss Sam Allardyce with a new dimension in attack and the player is confident he can combine well with England international Carroll.
"I know Andy Carroll," he told West Ham's official website. "He is a fantastic player and a centre forward who is physical and very important to the team.
"I hope I will play good football and reach the highest possible level. I am very confident I am going to succeed here.
"English football is beautiful. I always said I wanted to come back to England to play, and now I have this chance and I don't want to lose it."
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