Torres, 20, scored six goals and grabbed eight assists for Valencia in all competitions this season as they finished ninth in Spains La Liga.
The Spain youth international has agreed to a five-year deal with the Premier League club.
City has moved quickly to replace German winger Leroy Sane, who completed a move to Bundesliga champions, Bayern Munich, this month for 45 million euros plus add-ons.
City finished second in the Premier League this season behind Liverpool, and are still in the Champions League where they lead Real Madrid 2-1 ahead of their last-16 second-leg match in Manchester next week.
In another report, Real Madrid coach Zinedine Zidane has responded to growing transfer rumors that Barcelona legend, Lionel Messi, could leave the club after this season.
Messi has been at Barcelona since he was 12 and has won every laurel in club football while at the club side, but disagreements with head coach Quique Setien and recent disappointment in the champions league has made the striker question his loyalty to the club according to reports.