The 22-year-old Argentinean is highly rated after his exploits back home for All Boys and Boca Juniors, before scoring goals in Brazil for Sao Paulo over the past two years.
The forward's form attracted the attention of Chelsea, and some reports had even suggested that had a deal in place to sign him - but it is West Ham have who have brought him to Europe.
Slaven Bilic said: "We signed Calleri, unfortunately for him but good for us Argentina were knocked out of the Olympics last night, they didn't pass the group stage so he should be here with us – not today, not tomorrow, but pretty soon, depending on work permit or whatever.