The 23-year-old joins the Irons on a five-year contract, worth £30m plus £5m in performance-related bonuses and a 10 per cent cut of any future transfer.
West Ham announced the news late on Tuesday evening, possibly after sparking a frenzy in their online club shop earlier in the day by putting Scamacca's new number 7 shirt on general sale by mistake.
Scamacca scored 16 goals in Serie A last season and has made seven appearances for Italy.
The 6ft 5ins Italian will take the number 7 shirt that was vacated by recently released Ukraine international Andriy Yarmolenko.
"I am really excited to join West Ham," the forward told the club's official website. "I've waited a long time for this moment - it's been a dream to play in the Premier League.
"I feel like West Ham is the perfect team for me. They showed they really wanted me and when I spoke to the manager there was an instant understanding.
"I can't wait to play and show the supporters what I can do in the West Ham shirt - I hope we will love each other."
West Ham manager David Moyes was delighted with the signing as he continues to bolster his squad to once again compete in four major competitions.
"We've been looking to add more strength to our attacking options for a while, so we're delighted to have got Gianluca in," said Moyes.
"He comes really well recommended - and we're looking forward to working with him. He's a young centre-forward with a really bright future ahead of him."
Scamacca is West Ham's fourth major signing of the summer window after bringing in Morocco centre-back Nayef Aguerd, France goalkeeper Alphonse Areola and midfielder Flynn Downes to London Stadium.