His fellow Spaniard swapped the Estadio Ramon Sanchez Pizjuan for the Etihad Stadium in June and Negredo expects him to be "an important player" for Manuel Pellegrini's side.
"I've spoken with Jesus this morning and I am happy to be with him for another year," the striker told the press as he said goodbye to Sevilla on Wednesday.
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Negredo added his excitement at taking the chance to join the Premier League runners-up rather than let his career "stand still", with the City manager having answered all his questions.
"Pellegrini called me, we shared opinions and he convinced me about everything," the forward explained. "He told me what they could offer me there. It's a challenge for me and in this life you can't stand still.
"Now I start another journey and I'm very excited."
In his last appearance at the Sanchez Pizjuan, Negredo remarked that he owes a lot to the club president, Jose Maria del Nido, as he prepares for his next step.
"Thanks very much to everybody," he enthused. "It has been four fantastic years.
"I give thanks to the president for taking a chance on me. It was a dream. He has confided in me and given me a lot."