The 27-year-old, who scored 31 goals in 42 games for the Spanish outfit last season, will reportedly join for an initial figure of £21.5m plus add-ons.
Negredo is expected to undergo a medical examination with the Premier League outfit this week before officially penning terms on a reported four-year contract.
"It's official: Alvaro Negredo is a Manchester City player, short of doing the medical tests," read a statement on Sevilla's official website.
"Sevilla has organised a farewell gathering for the player at the Ramon Sanchez Pizjuan this evening at 18.30BST, so that those who have been his teammates 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."
City have also acquired Jesus Navas from Sevilla this summer.