Gattuso had not managed any other side after parting company with Napoli last summer.
The former Italy international was named as the new Fiorentina manager shortly after leaving Napoli but stepped down from the role without managing a single game following differences with the club's board over transfer targets.
Gattuso was also linked with a move to Tottenham Hotspurs last summer but the club's fans vetoed the move for his past declarations on racism, same-sex marriages and women in football.
Valencia finished ninth in the Spanish La Liga in the 2021/2022 campaign and severed ties with Jose Bordalas at the end of the campaign.
In a glossy promotional video announcing his arrival, he said: 'I experienced a respected Valencia. A team, together with the fans, everything connected by heart.
'For me, football means passion, it means respect for the game and love for playing with the ball.
'I know what it is like to fear Valencia, I have seen great teams fall at this stadium, which this season will be 100 years old. Valencianistas, let's experience this season with passion and let's enjoy the DNA of Valencia. I'm here.'
Gattuso's appointment has not gone down well with a number of Valencia fans, who have registered their anger with owner Peter Lim for the decision.
