Zarate is manager Sam Allardyce's first signing of the close-season and will move to Upton Park next month, with the club also agreeing a further one-year option for the 27-year-old.
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Zarate scored 20 goals in 35 games for Velez last season and will hope that form can help his second spell in the Premier League become a more fruitful one than his last.
He scored just four times in 14 appearances for Birmingham but Zarate is sure that he can bolster West Ham's forward options.
"This is a new chance for me and I want to play," he told the club's official website.
"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.
"If you ask me what I can bring to the squad then I say I hope I will bring goals. I will also bring dribbling skills and other attacking qualities.
"West Ham is a very important club and we know all about them and the Premier League in Argentina. This club is a beautiful club. I know English football from my time at Birmingham and I hope I will play well and reach the highest possible level.
"My aim is come here and do my best in order to help the club to climb as high as possible in the table and to reach European competition again."