The 25-year-old has agreed a three-year deal at the Etihad, according to the Australian side.
City's Brian Marwood told Melbourne City's official website: "Aaron is an extremely talented player who possesses the attributes we hope to foster and encourage within the City Football Group
"Aaron's move to Manchester allows us to further expose him to a high standard of opportunities to ensure his professional growth."
Melbourne head coach John van't Schip said: "Aaron was a fantastic contributor
He is deserving of his new opportunity and we wish him all the best for the future."
Fellow midfielders Luke Brattan and Anthony Caceres will head in the opposite direction on loan for the forthcoming season.
Source : PA
Source: PA