The influential Ivory Coast international, who turns 30 in May, has committed himself to City until 2017, ending speculation he could leave in the summer.
Mancini said: "I am happy because Yaya, for me, is one of the best players in the world and we are happy he plays for us and he stays here for another four years.
"I think it is very important for the club.
"I think that Yaya is a player that can play until 36, 37 because he can play in front of the defence, like a central defender, I think he can play every position."
The Italian expects more deals to be agreed with existing players in the coming months and two that could become a priority are Carlos Tevez and Gareth Barry, who will both enter the final years of their contracts in the summer.
Mancini said: "We have time to talk about this.
"Yaya was important - also for the other players it would be the same, in the next month, next two months. I am confident."