Vietto, 24, joined Atletico for 20 million euros (£17.8 million) in 2015 following a sensational first season in Spain with Villarreal but failed to adapt to Diego Simeone's side in two separate spells, sandwiched by a loan spell at Sevilla last season.
He scored 10 goals and provided five assists for Sevilla but not even Atletico's ban on registering new players until Jan. 1 helped him make an impact on his return to Simeone's side in August.
He made only seven starts in all competitions without scoring for Atletico this season and his departure was precipitated by the twin arrivals of Vitolo and Diego Costa after the club's ban on registering players expired.
At Valencia, Vietto will link up again with coach Marcelino, who got the best out of him at Villarreal, and the forward could make his debut at home to Girona on Saturday as Valencia's top scorer Simone Zaza is suspended.
(Reporting by Richard Martin, editing by Pritha Sarkar)
