The University of Edinburgh's £6.5 million plan aims to transform St Cecilia's Hall in the city into a centre for the study, display and enjoyment of instruments dating back to the 16th century.
It has now been awarded £823,500 by the Heritage Lottery Fund (HLF), which will fund new ways to make the instruments more readily available to the public.
The hall, which dates from 1763, is said to be home to one of the most important historic musical instrument collections anywhere in the world.
The refurbished and extended hall will be home to more than 1,000 objects and be a hub for research and teaching.
Jacky MacBeath, University of Edinburgh's head of museums, said: "We are absolutely thrilled with this award from the Heritage Lottery Fund.
"It is 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."
The plans, being developed by architects Page\Park, will reinstate the 18th-century character of the venue, restoring the original historic frontage on the Cowgate and repairing the external stonework.
A new entrance with a feature door will be visible from the Royal Mile. The oval concert hall at the heart of the building will be completely restored and the original acoustics will be recreated.
The venue will host live demonstrations, innovative use of sound and recordings, song-writing projects, exhibitions about instruments and their owners, resources for schools and lunchtime concerts.
The collection of instruments includes harpsichords, guitars, lutes and woodwind pieces.
According to its website, St Cecilia's Hall is the only place in the world where it is possible to hear 18th-century music in an 18th-century concert hall played on 18th-century instruments.
Colin McLean, head of the Heritage Lottery Fund in Scotland, said: "The collection of musical instruments is regarded as one of the finest in the world. HLF applauds the university's aspiration to bring this unique collection under one roof so that many more people can study, perform and enjoy it.
"We are also delighted to support the transformation of Scotland's oldest purpose-built concert hall. St Cecilia's Hall will have new life breathed into it as people explore the music that Scots have made over the centuries, while its new modern gallery will ensure that the collection is kept safe for future generations."
The hall is scheduled to close in mid-September for about 18 months, reopening in early to mid-2016.