The La Liga club announced the deal on their official website with the player set to undergo a medical at the Etihad Stadium in the coming days, although the finer details of the move have yet to be released.
A move to City for the Spain international had long been mooted, with new manager Manuel Pellegrini keen to add to his forward line following the sale of Carlos Tevez to Juventus.
"It's official: Alvaro Negredo is a Manchester City player, short of doing the medical tests," a club statement read.
"Sevilla has organised a farewell gathering for the player at the Ramon Sanchez Pizjuan this (Wednesday) evening at 19:30 (CET), so that those who have been his team-mates can say goodbye before leaving for (the pre-season tour of) South America.
"The Sevilla president, Jose Maria del Nido, will accompany the striker at this farewell."
Negredo joins Jesus Navas in making the switch from Sevilla to the Etihad Stadium, and will compete with the likes of Sergio Aguero and Edin Dzeko for a place in City's starting line-up.
Sevilla president Jose Maria del Nido had earlier suggested a deal was imminent for the 27-year-old.
Negredo was a key player for the team in La Liga season, notching 31 goals in 42 appearances as the club achieved a ninth-place finish.
The Spaniard joined Sevilla from Real Madrid in 2009, and was part of the team that lifted the Copa del Rey in 2010.comments