City could pay an additional €10-15 million in add-ons.
The 20-year-old has also agreed to terms on a five-year contract, The Guardian's Fabrizio Romano reports.
Valencia were forced to sell Torres because he had only a year remaining on his contract with Los Che and the option to leave on a free transfer next summer. He was previously valued at around €45 million.
City moved quickly to secure the player's services, beating Spanish giants Real Madrid and Barcelona to one of the country's biggest prospects. Torres, who has played six times for Spain's Under-21 side, earned plaudits during the 2019-20 season for his two-footedness and alertness off the ball.
Last October, he became the youngest player in club history to score in the Champions League, striking against Lille at 19 years old.
Leroy Sane's departure compelled City to seek reinforcements on the wing. A right-winger by trade, Torres can alternate on the left flank. He can expect competition for minutes from fellow right-side players Bernardo Silva and Riyad Mahrez.