The 26-year old is expected to sign a three-year deal worth 6.5million and join fellow Italian Gianfranco Zola at Upton Park.
Livorno president Aldo Spinelli said the deal was as good as done.
"It's practically done for Diamanti to West Ham," he said.
"The player deserves to make the step up after his stint at Livorno. Just a few details need to be finalised before the move becomes official."