"This is a new challenge and a new league for me. I have been doing well in the previous years and my goal is to go on and hopefully perform at the same level for City," Caballero told the club website.
"I know I am coming to a big club with a very good goalkeeper. City already have a great goalkeeper in Joe Hart, but I will try and compete for the no.1 spot. I will do my best in the training sessions."
Current City manager Manuel Pellegrini signed Caballero for Malaga from Elche when in charge of the La Liga side in 2011.
Before moving to Spain in 2004 Caballero won the Argentine championship, Copa Libertadores and Intercontinental Cup with Boca Juniors.
"The most beautiful moments of my career were under Manuel Pellegrini in Malaga, where we achieved big things and we made Malaga’s name known around Europe," he added.
No transfer fee was disclosed but media reports estimate City paid around six million pounds for Caballero, who has not played for his country at senior international level.
He is the third player to arrive at the Etihad Stadium since the end of last season, with Bacary Sagna joining on a free transfer from Arsenal and Fernando moving from Porto.
The club have moved ahead with their transfer plans despite being fined up to 60 million euros (47.71 million pounds) and having their squad capped for next season's Champions League after breaching UEFA's Financial Fair Play rules.
City open their title defence at Newcastle United on Aug. 16.
(Reporting by Josh Reich; editing by Amlan Chakraborty)
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