Russia winger Cheryshev, who starred for Valencia on loan last season, has signed a three-year deal.
Valencia said in a statement his contract includes an €80million buyout clause.
The Copa del Rey winner has reportedly paid less than the €7m that is said to have been the initial asking price for an outright purchase.
Cheryshev, 28, was unable to play in Valencia's Copa final win over LaLiga champions Barcelona as he was injured.
One of the stars of last year's World Cup, he impressed enough in 2018-2019 to earn a permanent move, one which has been set for completion since the announcement that an agreement in principle had been reached with Villarreal on 29 June.