Graham feels the Chilean will bring stability to City.
He told the Mirror: "I have seen what he has done and I am impressed. He seems the kind of manager who does not stand for any nonsense.
"He has also tasted life at a big club - maybe the biggest - when he was in charge at Real Madrid.
"I never saw Roberto Mancini as a long-term appointment - City were too often on the front pages rather than the back during his time there.
"But Pellegrini will bring some stability to City."