The Argentina striker will join the Hammers on a season-long loan.
West Ham United manager Slaven Bilic has told the club's official website that he is pleased to bring "top striker" Jonathan Calleri to the London Stadium after a deal to sign the Argentina star was agreed.
The Hammers will sign Calleri on a season-long loan deal subject to international clearance once the 22-year-old returns from his involvement at the Olympic Games in Rio de Janeiro.
Calleri has emerged as one of South America's top attacking talents in recent years as a result of his superb form for Boca Juniors and Sao Paulo.
Whilst at the latter club in Brazil, he hit 16 goals in 30 appearances including 12 strikes in the Copa Libertadores which saw him end as the competition's leading scorer in 2016.
A deal has now been struck which will see West Ham pay his current club, Deportivo Maldonado, a loan fee and he has already agreed personal terms over the move, with only international clearance needed to complete the transfer.
Hammers boss Bilic is pleased to get his man after a lengthy chase, and believes that Calleri's talents will bring balance to his front line.
The Croatian manager told the club's official website: "We have agreed to sign Calleri. Unfortunately for him, but good for us, Argentina were knocked out of the Olympics this week, so he should be here with us pretty soon, depending on the work permit.
"We did the deal a little while ago, and he is a top striker. You need a squad, of course, but it is all about the balance. I think we have a good balance."
The move comes despite a late report earlier this week that 11th-hour interest from Spanish giants Barcelona could railroad the deal.
Judging from Bilic's comments, Calleri's move to West Ham was already agreed by the time any interest from Barca surfaced, and he will be lining up alongside compatriot Manuel Lanzini in London this season.