Roar went into league administration days after winning Australia's top-flight A-League title in March after the previous owners racked up millions of dollars of debts.
Football Federation Australia, custodians of the financially shaky competition, would retain a 30 percent stake in Roar, the governing body said in a statement on Friday.
"We have been working extremely hard to find the right investors for last year's premiers and we believe we have found fantastic new owners in the Bakrie Group," FFA CEO Ben Buckley said.
"They have a strong background in football through ownership of several other clubs and their interests are in line with our outlook for the Roar."
The Bakrie Group, controlled by the family of Indonesia's Golkar Party Chairman Aburizal Bakrie, will hold their majority stake under a 10-year license through the group's sporting arm, Pelita Jaya Cronus.
Pelita Jaya Cronus already holds stakes in an Indonesian Super League club and Belgian second-division side Cercle Sportif Vise.
Dali Tahir, a former Asian soccer powerbroker and current member of FIFA's Ethics Committee, will chair the club.
The takeover comes two weeks after the FFA approved new owners for New Zealand-based Wellington Phoenix after their previous debt-stricken owner relinquished the license.
The 10-team A-League's seventh season kicks off on Saturday.
