The Spain international, who scored 25 goals in La Liga last season, is City's third summer signing, and their second from Sevilla, following the arrival of Jesus Navas and Fernandinho from Shakhtar Donetsk.
The 27-year-old will link up with the rest of the City squad for their ongoing pre-season tour of South Africa.
He should be joined shortly by another new attacking signing, Stevan Jovetic, who is expected to complete his move from Fiorentina soon.
A former Real Madrid player, Negredo rose to prominence at Almeria, where he scored 32 goals in his first two seasons at the club.
Sevilla broke their transfer record to recruit the player in 2009 and Negredo went on to score 70 goals in 139 appearances for Los Rojiblancos.
Negredo's move to City has been known for a short time after Sevilla held a "farewell" press conference for the player, who admitted he is relishing a fresh challenge at the Etihad.
"I think in football there are stages. For four years I have been very happy, but I think my time was over here," he told the club's website.
"I am happy to go to a big team."
Negredo has 14 international caps to his name and has scored six goals.
City will now likely turn their attention to finalising the signing of Jovetic after Fiorentina confirmed on Thursday that a deal had been agreed between the two clubs.
The Montenegro international is looking forward to linking up with Manuel Pellegrini's side and a reunion with his former Fiorentina team-mate Matija Nastasic.
"Florence will remain in my heart," the 23-year-old told firenzeviola.it. "I came here as a boy and I'm leaving as a man. This is a beautiful city and I was really fine.
"But I'm happy to go to City because they play in the Premier League and they are a very important team. I just want to win something.
"And then I'll find my great friend Nastasic.
"I will be leaving a very strong Fiorentina and I'm happy about that. I wish that they can win the scudetto.
"It would have been nice to play with Mario Gomez, but I wanted a change of scenery.
"I know that Fiorentina's fans are a little angry with me, it's normal, but I have never said anything bad, either about them or about Fiorentina."
Viola coach Vincenzo Montella added: "Stevan gave so much to Fiorentina, but he had expressed a desire to grow elsewhere and I wish him good luck."