The former Manchester United forward, who played under the Chilean at Real Madrid and Malaga, believes that given time he will be a success with his old club's bitter rivals
Van Nistelrooy played under the 59-year-old Chilean at both Real Madrid and Malaga and has backed him to improve the team, building on the work of Roberto Mancini.
The ex-Netherlands striker reckons Pellegrini's approach to management and his style of play will be a welcome change to what the City players will have been used to under the Italian.
"I can only talk from my own experience - half a season under him at Madrid and the last season of my career at Malaga," Van Nistelrooy told reporters.
"The experience was really good and on a professional level and a personal level I rate him very highly.
"I think he proved at Villarreal and with Malaga showed that he can build a new team and get things moving. He can create a structure and culture at the club whereby things get better.
"So in that sense - and even though this is me speaking as an ex-United player - I think he will build something at City.
"I don’t know what his plans are for City, I only know the way he has worked in the past. I know him as a person and, for me, he’s up there with the best.
"He dealt with the expectation at Madrid. He got a record number of points for them in the season he was there.
"I think he’s used to expectation and the fact is he’s got so much experience over the years, so I don’t think the pressure will be a problem for him.
"I think with the squad City have and with him in charge - he will maybe need a bit of time - but I think they will do well."