The 23-year-old has joined on a five-year contract with the option to extend for a further year.
Scamacca was the second top scoring Italian in Serie A last season with 16 goals from 36 appearances and had attracted interest from Paris Saint Germain.
Scamacca is West Ham United's fourth summer signing as they look to improve on last season's seventh place finish and impress in the UEFA Conference League.
The Hammers have already signed goalkeeper Alphonse Areola on a permanent deal from PSG following a loan spell and added Nayef Aguerd and Flynn Downes as well.
Scamacca, who has been handed the number seven shirt, said: "I am really excited to join West Ham. 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 boss David Moyes added: "We've been looking to add more strength to our attacking options for a while, so we're delighted to have got Gianluca in. 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 yet to score in seven appearances for the Italian national team.