Sevilla announced Negredo would join City, pending a medical, and held a "farewell" press conference for their star striker on Wednesday evening.
Negredo, who scored 25 Primera Division goals last season and whose transfer will cost a reported 23 million euros (£20million), said on the club's official website: "I think in football there are stages. For four years I have been very happy, but I think my time was here over.
"I am happy to go to a big team."
The 27-year-old paid an emotional tribute to Sevilla for "four fantastic years" and added: "For me this will be my home for a lifetime."
But he revealed he was relishing the chance to link up again with Jesus Navas, who has already moved to the Etihad from the Andalucian club.
He said: "I am happy to be spending another year with him."
Sevilla president Jose Maria del Nido earlier revealed Negredo would sign the "contract of his life" at City.
He said: "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."
Should the deal go through, Negredo would become new City boss Manuel Pellegrini's third signing of the summer following the arrivals of Navas and Brazilian midfielder Fernandinho.