The grant from the Heritage Lottery Fund (HLF) will go towards the £6.5 million cost of redeveloping St Cecilia's Hall in Edinburgh's Old Town.
Named after the patron saint of music and built in 1763, it is the oldest purpose-built concert hall in Scotland and the third-oldest in the world.
The building is part of Edinburgh University, a leader in musical instrument research, and is home to one of the world's most important historic musical instrument collections.
Jacky MacBeath, head of museums and deputy head of the centre for research collections at Edinburgh University, said: "We are absolutely thrilled with this award from the Heritage Lottery Fund. It's a huge boost to the project, which focuses on revealing St Cecilia's Hall as one of the Old Town's most important historic places, transforming access to this special building and its unique collections of international significance."
Among its rare instruments are harpsichords, virginals, spinets, organs and fortepianos - some about 400 years old - as well as harps, lutes and citterns.
The £823,500 grant from the HLF will fund new ways for audiences to enjoy and experience the instruments. Curators want to have live demonstrations of them being played, make recordings available to the public, put on exhibitions about the instruments and their owners, and run song-writing projects.
The grant comes in addition to an earlier £76,500 development award by the HLF.
Images of how the building will look once the work has been completed were revealed last year.
The overhaul will include the creation of a harpsichord-shaped entrance gate designed to draw visitors from the Royal Mile, a 40% expansion of gallery space and improved acoustics and sound-proofing. A redesign of the building's main concert hall to restore its original oval shape - allowing musicians to perform on a raised stage or surrounded by audiences - is also included.
Announcing the earlier award, Colin McLean, head of the HLF in Scotland, said: "The University of Edinburgh's collection of musical instruments is regarded as one of the finest in the world."
Work on the project is due to begin this autumn and the university believes the revamp will preserve the hall for the next 200 years and attract visitors with a general interest in music in addition to specialists.
As well as displaying historic musical instruments, the hall's curators also want to be able to exhibit more modern pieces such as famous rock guitars.