No fee was confirmed by either club, but it is thought City have paid Atletico Madrid £35million for Aguero, eclipsing their previous high of £32.5million for Brazil forward Robinho in August 2008.
"I don't think I'll have too many problems settling into the team," he told City's official website.
"I'll obviously be doing my best to do what the manager asks and try to work the way he wants me to, and of course he will know how he wants to use me.
"Once I'm out on the field I will get to know my way round, but I can't say that for sure because I have not even made my debut yet.
"But I'm sure everything will be fine. I'm going to be relaxed about it."