The 25-year-old has scored five goals in 16 caps for his country and holds the A-League record for most assists in a single season when he created 21 goals for his teammates in 2014.
Mooy arrives with a big reputation in Australia having twice been named Melbourne's player of the year, but it remains to be seen whether he will be able to cut it at an undeniably higher level in the Premier League.
"Aaron is an extremely talented player who possesses the attributes we hope to foster and encourage within the City Football Group," the Citizens managing director of football services Brian Marwood told Melbourne's official website.
"Aaron's move to Manchester allows us to further expose him to a high standard of opportunities to ensure his professional growth."
Fellow Australians Anthony Caceres and Luke Bratton will go the other way, joining Melbourne on loan for the season.