Zarate signed for West Ham on Wednesday, having previously played in the Premier League for Birmingham City, and Allardyce is confident that the striker's record in Argentina will translate to the English top flight this time.
"This signing is based on his record from being in Argentina, where he has scored the goals that he has scored because we are looking for some goals," Allardyce told the club's official website. "Plus the fact that, at a much younger age, he had the experience of the Premier League with Birmingham for a while.
"We hope that a combination of the two - the fact that he knows the Premier League and now he has become more experienced and more mature, he is going to have evolved in terms of giving us a few more goals in the Premier League when he gets the opportunity.
"Hopefully he is going to settle in quickly and bring us those sort of options that we need to be more successful in terms of goalscoring next season."
West Ham finished 13th in the Premier League last season.