The Argentinian goalkeeper this week joined the Barclays Premier League champions in a £4.4million move from Spanish outfit Malaga.
The 32-year-old will provide competition for first-choice Joe Hart, the England number one, at the Etihad Stadium.
Caballero, who will replace released Romanian Costel Pantilimon in the squad, said: "I knew that Manchester City were interested in me so I tried to do my best for my previous club to make the move to a very big club possible, and finally it's a reality and I will try to prove myself."
Even though he has principally been signed as back-up to Hart, Caballero hopes he can push on at City and earn full international recognition.
Caballero won the Under-20 World Cup with Argentina in 2001 and was also a member of the 2004 Olympic gold medal-winning squad.
He said: "The first goal is to do things well and show why City were interested in me.
"Obviously it would be good to get back with the national team and hopefully I can achieve that."
Caballero believes playing under Manuel Pellegrini, his former manager at Malaga, will give him the confidence to succeed.
Getting the chance to work with Pellegrini again was one of the main attractions of City to Caballero.
Pellegrini signed the former Boca Juniors keeper for Malaga from Elche in 2011.
He went on to become a key figure in the Andalusian club's rise to prominence in Spain, which included a run to the Champions League quarter-finals in 2013.
Caballero, who is City's third summer signing after Bacary Sagna and Fernando, said: "I think his best quality is giving players the confidence to achieve their potential."