"If you ask me what I can bring to the squad then I say I hope I will bring goals," Zarate told the club's website.
"I will also bring dribbling skills and other attacking qualities."
West Ham could certainly do with a bit more firepower up front after scoring just 40 goals in 38 Premier League matches last season as they finished 13th.
Zarate turned down a chance to play for his father's country, Chile, at the World Cup earlier this year and was also approached by Italy, his mother's country, in 2009.
A former under-20 international, his chances of making the Argentine squad for the World Cup were always slim with Sergio Aguero, Lionel Messi, Gonzalo Higuain, Ezequiel Lavezzi and Rodrigo Palacio all ahead of him in the pecking order.
(Reporting by Nick Mulvenney in Sydney, editing by Greg Stutchbury)
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