City councillors agreed permission should last for seven years instead of the normal three to give the project the maximum chance of completion.
The unanimous decision comes as rival developers mount an appeal against the council’s refusal of controversial proposals to turn the landmark building into a £75 million luxury hotel.
Despite the approval of the music school plans, St Mary’s currently has no right to the building because of an existing agreement between the council and hotel developers Duddingston House Properties, which it is understood may not expire until 2022.
Planning convener Ian Perry said the committee had agreed to a seven-year expiry on consent for the music school because of the unique situation with the other application being appealed.
“That will need to run its course,” he said. “It’s not unusual in the circumstances to give a developer extra time.”
William Gray Muir, chairman of the Royal High School Preservation Trust, which is behind the music school plans, said they had a wonderful opportunity to transform a building at risk into a dynamic asset for the city.
He said: “We are delighted our proposals have received unanimous cross-party approval, with the council granting us a special, extended seven-year timescale for planning and listed building consent.”
He said they had asked for the seven-year approval because of the “contractual uncertainty” about the future of the building”.
The trust has made a £1.5m offer for the building and Mr Muir said the proposals were fully funded.
Planning officials had recommended approval of the St Mary’s plans, which include an extension to the east of the site and demolition of some listed structures, including the former gymnasium block and lunch hall.
The former library and headmaster’s study would be converted into publicly-available studio space, while the south-facing car park would be become publicly-accessible gardens with room for performance space.
Mr Muir said: “We have had the support of the broadest possible range of heritage, amenity and citizens’ groups.
He added: “This project seems to be something which has really caught people’s imagination.”