The two teams were locked in negotiations all of Monday before a new deal was reportedly clinched by City.
The Spanish side held out to cash in on the 27-year-old, finally thrashing out a deal worth around £24m.
City's original offer of £21m was rejected and the club will now pay the extra transfer fee through variables relating to performance and titles earned.
Negredo looks set to sign a four-year-deal with the club, thought to be worth around £3.9m.“Manchester City look to be close to completing a deal for Alvaro Negredo”
The president of Sevilla Del Nido was reported as saying recently: "Sevilla have put an evaluation on Negredo and either Sevilla are paid what they're asking for or he stays for another three years.
"We are in no hurry. We are in a better situation than a month ago and we've shown that with the signings that we've made."
It follows reports that City boss Manuel Pellegrini has moved his attention firmly to securing the striker, having missed out on Paris Saint-Germain bound forward Edinson Cavani.