Turner Prize winners Tracey Emin, Antony Gormley, Douglas Gordon, Martin Boyce, Jeremy Deller and Anish Kapoor have also put their names to an open letter urging the Royal Botanic Garden to reopen Inverleith House.
It warns that the permanent closure of the gallery is of “international cultural significance” and will also represent an “enormous loss to Scottish culture”.
Inverleith House is believed to have staged more exhibitions by Turner Prize winners and nominees than any other gallery in the UK, apart from the Tate in London.
Botanics chiefs have been under mounting pressure since they announced the end of regular exhibitions after it was decided to explore alternative uses for the 18th century building, which was closed at the end of last month.
More than 9,000 people have backed an online petition calling for “one of the city’s best-loved and most significant arts spaces” to remain open, while around 700 protesters turned out to demonstrate on the final day of a special 30th anniversary exhibition.
The open letter has been sent to two Scottish Government ministers responsible for the Botanics - culture secretary Fiona Hyslop and environment secretary Roseanna Cunningham.
Creative Scotland has also been urged to intervene over the fate of Inverleith House, which had a bid for long-term funding turned town by the arts agency in 2014. However the Botanics was given special funding by the quango last October for a series of special anniversary projects, including a study into the long-term future of exhibitions there.
Ms Hyslop called a summit last week of senior figures at the Botanics and Creative Scotland to discuss the future of Inverleith House, a meeting described as "constructive" by the Scottish Government.
Other signatories include the Scottish authors Ian Rankin and Ali Smith, art philanthropist Anthony d'Offay, fashion designer Pam Hogg, and the Scottish artists Nathan Coley, Graham Fagen, Toby Paterson, Alison Watt, Luke Fowler and Jim Lambie.
The open letter calls for the board of trustees of the Botanics to agree to an "open debate" on the future of Inverleith House at its next meeting in December.
It states: “Over the last 30 years, Inverleith House has attained a world-class reputation for both its programming and its incomparable beauty as a space for viewing contemporary art and botanical exhibitions.
“Paul Nesbitt (exhibitions director) and his team have shone a light on otherwise unseen archival botanical materials, nurtured Scottish artists at key moments in their careers and brought the work of ground breaking international artists to the UK.
“This remarkable achievement has been accomplished with minimal staffing and modest financial support.
"While we accept that the future of Inverleith House falls within the jurisdiction of the Royal Botanic Garden, we feel that its loss is of international cultural significance.
"In light of wide spread public dismay, we ask that the decision to bring to an end 30 years of contemporary art programming at Inverleith House be reopened for debate at the next meeting of the board of trustees in December and that the wider community be given an opportunity to participate.
"We also urge the board to work in cooperation with Creative Scotland to seek ways of securing the long-term future of Inverleith House as a contemporary art gallery, a future that reflects its 30 years of excellence in visual art and botanical programming.
"Inverleith House is not just a contemporary art gallery; it is a national treasure and an international beacon of our culture. Closing the doors of this cultural asset with no plans for the future of the building is unthinkable and leaves us all diminished.
"We sign this letter in order to preserve its unique place in our culture for this and future generations."
However a joint statement issued by Sir Muir Russell, chair of the board of trustees, and Simon Milne, regius keeper, in the response to the letter, fell short of promising to rethink the closure of the gallery.
The statement said: “The letter shows the high regard in which Inverleith House Gallery has been held. We will continue to use both the overall setting of the Garden and indoor spaces to engage our visitors with art in the garden environment.
"The intention is very much that we intend to retain our reputation as an art venue across the board, be it for botanical art, illustration, performance, photography, sculpture and contemporary art.
"We welcome the opportunity to discuss with Creative Scotland the options to achieve this."
A spokesman for the Scottish Government said: “The cabinet secretary for culture held a meeting with the chairs and chief executives of Creative Scotland and the Royal Botanic Garden last week to discuss options for the future of art in the garden. The meeting was constructive and discussions are on-going.”
A spokesman for Creative Scotland said: “We remain disappointed at the decision to cease operating Inverleith House as a dedicated contemporary art gallery. However, we are in discussions with the Royal Botanic Garden to explore options for a positive future."