After struggling to make an impact on and off the field since making their debut in the competition in 2010, Heart had been the subject of a bid from Victorian Premier League club South Melbourne last year.
The club sacked 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 new record of 20 consecutive matches without a win, beating the Newcastle Jets last Friday.
But the struggling outfit are now set to receive an enormous boost, with City – owned by a member of the United Arab Emirates' ruling family – set to provide a major influx of business and football expertise.
"We are excited about the opportunity to make Melbourne Heart one of the most successful football clubs in Australia and throughout the region," City chief executive officer 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."
According to joint statements released by City and Heart, Van 't Schip and the existing Heart playing staff are set to stay in place for now, with no major announcements about changes to be made until 'mid-2014'.
"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 said.
Football Federation Australia chief executive David Gallop heralded the announcement as an indication of the A-League's continuing growth.
"Football has moved into the mainstream of Australian sport and is ideally placed to benefit from the boom in football across Asia," Gallop 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 have also expanded into North America, with New York City set to make their Major League Soccer debut in 2015.
