The Uruguay international, who had also been strongly linked with West Ham United, moves to Mestalla on a five-year contract that includes a €140 million ($225.8 million) release clause.
Valencia has reportedly paid a fee in the region of €14.5 million ($23.4 million) for the 22-year-old, while Celta has confirmed the return of Santi Mina as part of the transfer.
Jorge Saenz is also expected to head to Balaidos on a two-year loan.
Mina made more than 100 league appearances for Valencia and scored 29 goals, but he is now back at Celta after four seasons away.
Marcelino's side saw off competition for the signing of Gomez, whose release clause has been set at €140 million, with Barcelona also rumoured to have showed an interest this year.
He scored 30 goals in 71 league games for Celta after joining from Defensor Sporting two years ago.
Valencia has been busy during the close season having also added the likes of Jasper Cillessen, Manu Vallejo and Jason to their squad, while Denis Cheryshev has signed a permanent deal.