Sir David had been under pressure from Bank of Scotland to offload assets, including Rangers.
He subsequently sold metals and property businesses and his call centre operation.
A resolution was passed at a meeting of Murray Group Management Limited, formerly Murray International Holdings, which stated: “That it has been proved to the satisfaction of this meeting that the company cannot by reason of its liabilities continue its business and that it is advisable to wind up the same”.
John Charles Reid and Christopher McKay of Deloitte have been appointed joint liquidators.
The headquarters of the Murray empire in Charlotte Square, Edinburgh closed in September with the business shouldering £300m of debts. He also put his £2m home in Murrayfield up for sale.