Reports suggest that La Viola paid the Hammers a fee of £1.6million for Zarate's services.
The Argentine took to Twitter to thank the London club and its fans for their support during his time in the Premier League.
"I would like to thank David Sullivan and David Gold for believing in me and for giving me the opportunity of playing at such a special club like West Ham," Zarate said via his official Twitter account.
"I would also like to thank my team-mates for the good times we shared and wish them the very best for the future, and especially I would like to thank from the bottom of my heart all the West Ham supporters for their unconditional support and affection, you are truly unique.
"Thank you all very much! COYI."
Thanks !! pic.twitter.com/7rODbOBvSa
— Mauro Zarate (@mau_zeta) January 21, 2016