The Italian has agreed to a contract that will tie him to the club until June 2021, when he will be aged 30.
Juventus released financial details of the transfer, with the initial fee totalling €16 million to be paid in installments over two years, and then an additional €2 million set to be received if certain conditions are met.
Zaza linked up with Valencia on loan following a torrid temporary spell with West Ham United in the first half of the season. He wasn't able to score for the Premier League outfit in 11 matches, but has scored four goals in 14 La Liga games. He netted a quickfire brace in Sunday's 3-1 win at Granada, and notably pocketed a sublime hit against Real Madrid in February.
The 25-year-old rose to prominence at Sassuolo, where 20 goals over the course of two seasons helped firmly establish the minnow in Serie A. It was there that he showed his knack for dispatching superb strikes, encouraging Juventus to exercise an option on its co-ownership agreement with Sassuolo to acquire Zaza for €18 million in 2015.
Zaza has won 16 caps and scored two goals for Italy, but inadvertently became an internet sensation when his peculiar run-up and skied penalty in the shootout against Germany in Euro 2016 led to his country's elimination from the tournament. He issued a public apology following the gaffe.