The former Malaga boss has signed a three-year deal with the FA Cup finalists, who are odds-on (8/13) to win any trophy next season and 6/5 to go without.
Pellegrini is 8/1 to win August's Premier League Manager of the Month award and 9/1 not to win any of his opening three league games in charge and 14/1 to have left the club by Christmas.
Sky Bet's Chris Spicer said: "It seems City have hired Pellegrini with his credible Champions League record in mind and we now go 10/1 that they win the tournament.
"They're 22/1 to produce a Champions League and Premier League double, or punters can simply back City to win any two major trophies at 7/1."