The 27-year-old has signed a three-year contract, with the option of a further year, as Allardyce strengthens his forward options after a troubled 2013-14 campaign in that department for the Hammers.
"My reaction is that I am very happy to be at West Ham," said the forward in a press release.
The Hammers' big-money buy last summer, Andy Carroll, spent half of the campaign on the sidelines through injury to leave Allardyce short of options up front and then, on his return, the England international only scored two goals.
Allardyce, however, has wasted no time in finding support for Carroll with the deal for Zarate.
It will be Zarate's second taste of top-flight football in England having played on loan for Birmingham for four months in 2008, scoring four goals in 14 appearances, but he was unable to prevent the Blues from being relegated at the end of that season.
"This is a new chance for me and I want to play," added Zarate, who scored 20 goals in 35 matches in all competitions for Velez last season.
"I think I played well for Velez this season and that was important for me
I had some good team-mates and they helped to make it a fantastic season for me.
"I know English football from my time at Birmingham and I hope I will play well and reach the highest possible level."
Zarate is a controversial figure as in 2010 while with Lazio, and on suspension for two games for insulting a referee, he was photographed giving a fascist salute.
Standing with Lazio's infamous 'Ultras' section of fans in watching a loss to Bari, Zarate's spokesperson claimed the player was unaware of the significance of his actions.
In April last year, Zarate was supposed to be in Argentina receiving treatment for a skin condition after presenting the club with a doctor's note, only to be spotted on holiday in the Maldives.
At the time Zarate was not training with the first team due to persistent disciplinary issues.
It was at the end of the 2012-13 season, after spending four years with Lazio that included a spell on loan with Inter Milan, that Zarate returned to his first club Velez.
In his first spell, Zarate scored 28 goals in 99 appearances, and then last season he finished as leading scorer in the Clausura with 13 goals in 19 appearances, prompting Allardyce to bring the forward to Upton Park.
Source : PA
Source: PA