Sky Sports revealed earlier this week that the Hammers were in talks with the 27-year-old former Birmingham front-man.
Now West Ham have won the race for his signature, with the player expected in England in the next 48 hours.
Sky Sports understand that Zarate has agreed a three-year deal to move to Upton Park.
Zarate returned to Velez Sarsfield from Lazio last year and has just finished the Argentine season as top-scorer.
A source told Sky Sports: "Mauro is very excited about a move to England, he enjoyed his spell last time with Birmingham and is ready to play in the Premier League again."