The 22-year-old shone, during a six-month loan to the Brazilian club, was top scorer with nine goals in the Copa Libertadores, South America's top club competition, reports Xinhua news agency.
ESPN reported on Monday that Uruguayan outfit Deportivo Maldonado, who own Calleri's economic rights, agreed to a year-long loan with the Premier League club.
"The transfer to West Ham is already completed," Calleri was quoted as saying. "I hope I can adapt as soon as possible to the Premier League."
Calleri is expected to feature prominently for Argentina in the Rio Olympics. Argentina's first match will be against Portugal at Rio's Olympic stadium on August 4.
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