Zaza joined the club on loan from Juventus in January, with Valencia holding the option to sign him for an initial fee of €16million - a clause they have now activated.
Valencia may have to pay a further €2m depending on the 25-year-old's success in La Liga.
Having already paid a €2m loan fee for Zaza, the potential total cost of his acquisition could be €20m.
The club's sporting director Jose Ramon Alesanco revealed last month that an agreement to take up their option had been reached and that was confirmed on Monday.
"Simone Zaza will become property of Valencia CF from July 1, with a contract until June 2021, under the terms of the agreement signed with Juventus," read Valencia's statement.
Zaza spent a miserable first half of the season on loan at Premier League side West Ham, where he played eight times in the top-flight without scoring, prompting them to terminate his stay prematurely and pass on their option for a permanent deal.
But the striker, who infamously missed a penalty for Italy in their Euro 2016 quarter-final shoot-out defeat to Germany, has scored four goals in 14 appearances since arriving at Valencia, including a strike in their February victory over Real Madrid and a double in Sunday's 3-1 win at Granada.
Los Che have moved clear of the relegation zone since Zaza's arrival and now sit 12th in LaLiga after a run of three consecutive victories this month.