Work at the quarry, which supplied the stone for the September 2011 memorial in New York, would have ended in December next year had an extension to planning permission not been granted.
The Quarry was the subject of a renewal application at the planning and regulatory services committee on Tuesday when members agreed to extend permission for works until 2031.
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Members were told that there had been no objections to the renewal application and the committee subsequently agreed unanimously to the extension. Heldon and Laich councillor John Cowe said the stone produced had become "world renowned".
He said: "Hopeman stone is world-renowned and was used in the memorial for 9/11 in New York. I am delighted to see that it can be extended for a further 15 years."
As well as the New York memorial, stone from the quarry was used in the memorial for victims of the Dunblane massacre. It was also used for creating the work on the Royal Museum of Scotland in Edinburgh.
The quarry is operated by Moray Stone Cutters, who in 2005 won a contract to supply sandstone for the restoration and repair of the Gothic Cathedral in Barcelona.
(MH/CD)
