City, owned by Abu Dhabi billionaire Sheikh Mansour bin Zayed Al Nahyan, have big plans for the Melbourne outfit which languishes at the bottom of the A-League table.
The new owners, who include a consortium led by City that features the ownership group of the Melbourne Storm rugby league team, paid about AUD $11 million (USD $9.7 million), Australian Associated Press reported.
"We are excited about the opportunity to make Melbourne Heart one of the most successful football clubs in Australia and throughout the region," City CEO Ferran 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.
"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."
Bart Campbell, chairman of the holding company Heart Consortium Group and also the Storm's chairman, added: "It is our shared ambition to replicate the model that City created with the New York Yankees around New York City FC, and for both organisations to benefit as a result."
The Heart and Storm will remain separate entities.
Vote of Confidence
FFA chief executive David Gallop said the buyout was a huge vote of confidence in the future of the A-League.
"The arrangements we have approved will see Manchester City have an 80 per cent share," said Gallop of discussions launched more than a year ago in New York.
"Football has moved into the mainstream of Australian sport and is ideally placed to benefit from the boom in football across Asia," he added.
"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."
Gallop said the consortium would bring a "high level of expertise in football and sports business matters, and that can only strengthen the Melbourne Heart and the Hyundai A-League as a whole."
"The new owners are taking a long-term view of this investment, which fits perfectly with our strategic plans for the A-League and the growth trajectory of Australian football," he said.
City's investment in the Heart follows its establishment of New York City Football Club in May 2013, which will enter Major League Soccer in the United States in the 2015 season.
Heart sacked coach John Aloisi in December after a terrible start to the season. The club brought back his predecessor John van't Schip and just missed a record run of 20 consecutive matches without a win by beating the Newcastle Jets 3-1 last Friday.
After that first win of the season, Heart have eight points from 15 games - nine points fewer than second-from-last-ranked Wellington Phoenix.
The new owners said there would not be any major announcements until mid-2014, out of respect for the coaching staff and players.