Calleri has joined the east London Club on a season-long loan and has been granted international clearance.
The Argentine forward is available to face Astra Giurgiu in the Europa League on Thursday night and Mr Sullivan is expecting big things from the talented forward.
Mr Sullivan said: “He's a top player and was the leading goalscorer this season in the Copa Libertadores, the South American version of the Champions League.
“He is the immediate back up for Argentina who are the number one rated team in the world.
“He showed his quality at the Olympic Games for Argentina this summer and will be another great addition to the squad.
“We have a great track record of signing players from Argentina with Carlos Tevez and Manuel Lanzini becoming big players at West Ham United. It would be great if Jonathan could follow in their footsteps.
“We expect him to be one of our top goalscorers this season.”