Spain international Negredo, who scored 25 Primera Division goals last season, is set to join the Premier League runners-up for a reported fee of 23million euros (£20million), with only the expected formality of a medical to be completed.
The 27-year-old will link up with former team-mate Jesus Navas, who moved to the Etihad Stadium from Andalucia earlier this summer in a £15m deal.
Sevilla held a "farewell" press conference for Negredo, who admitted he is relishing a fresh challenge at City following his successful spell at Sevilla.
"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."
He also paid tribute to his club for "four fantastic years" and added: "For me this will be my home for a lifetime."
A Sevilla statement read: "It's official: Alvaro Negredo is the new player of Manchester City, pending medical examinations, so Sevilla FC have organised a farewell ceremony at the Ramon Sanchez Pizjuan for Wednesday evening.
"Sevilla president Jose Maria del Nido will accompany the striker as he bids farewell."
Earlier on Wednesday, Del Nido said: "We are about to close on the sale of the player and, if everything goes normally and everything is signed, he will soon say goodbye to the Ramon Sanchez Pizjuan.
"Manchester City are buying a great player, the top-scoring Spaniard in La Liga. This is a big deal for Sevilla, the second most important in our history after we sold (now-Barcelona full-back) Daniel Alves, and the player will sign the contract of his life.
"Everyone should be happy; it is a great deal for all three parties."