The 20-year-old came through Valencia's renowned academy and scored four times in 34 appearances last season as they finished ninth in La Liga.
He is considered one of Spain's brightest young prospects but Valencia needed to sell some players to balance their books, even before the financial impact of coronavirus.
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Torres told Man City's club website: "I am so happy to be joining City. Every player wants to be involved in attacking teams and Manchester City are one of the most attacking in world football.
"Pep (Guardiola) encourages a really open, aggressive style, which I love, and he is a manager with a proven track record of improving players. To have him overseeing my development is a dream.
"City have won plenty of trophies in the last 10 years and I hope I can play a role in continuing that success."
Torres made his senior debut as a teenager during the 2017-18 season, going onto make 13 appearances in total that term. The following season he scored three times in 37 games in all competitions as Valencia won the Copa del Rey.
City are also in the market for centre-backs this summer and have had a £41m offer for Nathan Ake accepted by Bournemouth.
Source: skysports
