The 2.8 million plans for the Festival Theatre will create a separate rehearsal space for theatre and dance acts that can also be used as a venue for up to 160 spectators.
The space - within a new four-storey building on a gap site to the rear of the Nicolson Street venue - will also include a small foyer and a box office.
A seven-storey high block of flats for 146 students will also be built, but the plans have angered two of the Capital's leading heritage groups.
The Architectural Heritage Society of Scotland (AHSS) said that the student flats are too tall and will detract from views of the dome at the nearby Old College of Edinburgh University.
The Cockburn Association said it was "uninspired" by the "mediocre" theatre extension.
Euan Leitch, a member of the Forth and Borders cases panel for the AHSS, said: "We welcome the creation of new build on the long vacant site but have some concerns over the height and design detail of the student accommodation proposed."
Marion Williams, director at the Cockburn Association, said: "Edinburgh is known to have more theatre seats per head of population than any other city in the UK. We are concerned that another public performance space will only exacerbate the present situation."
She added that the heritage group - whose president is former Standard Life boss Sandy Crombie - is "uninspired" by the rehearsal room extension, which she said is "reminiscent of a mediocre station upgrade scheme from the 1970s".
The extension includes some commercial office space and meeting rooms on the ground floor, with rehearsal rooms and a foyer on the second floor and retractable seating and dressing rooms above.
Nobody at the Festival Theatre Trust was available to comment about the plans today.
However, Mark James Price, planning and heritage adviser at The Theatres Trust, said: "Theatres need substantial development if they are to keep pace with the public's expectations and the needs of performers and producers.
"The new rehearsal space is long overdue and will enable the theatre to provide world class standard facilities."
In a report for councillors, John Bury, the council's head of planning, recommended that the scheme is approved.
He said: "The ability to cater for a wider range of high quality acts will help further enhance Edinburgh's reputation as a cultural city."