Owners MAMA & Company have accepted an offer for the 1500-capacity venue, with the final gig due to be held on December 31st 2013.
All events before, and including December 31st, will go ahead as scheduled, with the sale due to be completed on January 6th 2014.
It is understood that the new owners will close the building for refurbishment and are not thought to be reopening it as a music venue.
Acts including Adam Ant, Miles Kane and Edinburgh’s Nina Nesbitt were all scheduled to perform at the Lothian Road venue next year.
The B-listed building was bought in March 2008 from Luminar Liquid Ltd, and opened as a live music venue in September that year.
A spokesman for the firm said: “We would like to take this opportunity to thank the public, the venue staff, and all the great artists and promoters who have graced the stage over the last five years for their support.
“We understand that the new owners will close for refurbishment on that date and are not expected to re-open as a music venue.”