Zaza scored five Serie A goals in 19 games last season and also struck Juve's winner in their friendly win over West Ham at the London Stadium earlier this month. The 25-year-old was in Italy squad for Euro 2016.
A permanent fee of £20 million will be automatically triggered if the striker makes a certain number of Premier League appearances this season, plus a further three million pounds in contingent payments, the east London club said.
"I want to thank everyone for welcoming me... I wanted to start a new experience and I feel this is the right choice for me," Zaza told the club's website (www.whufc.com).
"I have been fortunate enough to have already played at the new stadium with a different shirt. It is a beautiful stadium and I felt the warmth of the fans and this was a big reason why I wanted to join the club."
West Ham, who failed to make the Europa League group stage for the second year in a row after being eliminated by Astra Giurgiu, face Manchester City away in the league later on Sunday.
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