The club fired coach John Aloisi in December following a disastrous start to the 2013-14 campaign, replacing him with predecessor John van't Schip, and only narrowly avoided setting a record of 20 consecutive matches without a win by defeating the Newcastle Jets on Friday.
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But the struggling outfit is now set to receive an enormous financial boost, and City CEO Ferran Soriano is setting high targets for the acquisition.
"We are excited about the opportunity to make Melbourne Heart one of the most successful football clubs in Australia and throughout the region," Soriano said in a statement. "We believe the strong sports culture of Melbourne, combined with the football and commercial expertise within our consortium, will make for a powerful combination both on and off the pitch."
According to joint statements released by City and Heart, Van't Schip and the current players in Melbourne are staying put for now, with no major announcements being made until the middle of the year.
"The first thing we must do is take the time to listen and learn and then to develop our strategy for strengthening the club over time," Soriano added.
Football Federation Australia chief executive David Gallop said he was delighted with the announcement, saying it shows how much the A-League is growing.
"Football has moved into the mainstream of Australian sport and is ideally placed to benefit from the boom in football across Asia," he said. "Manchester City and their Australian partners have made a strategic investment and I welcome them to our growing competition. It's another sign that the world is taking notice of Australian football."
Manchester City has also expanded into the USA, joining forces with the New York Yankess to form New York City FC, which is set to make its MLS debut in 2015.