The group, headed by brothers Chris and Jeff Galvin, opened Pompadour restaurant and Galvin Brasserie de Luxe at the five-AA-star hotel in Princes Street in 2012.
In a statement Galvin Restaurants said: "Our arrangement will come to a close by mutual agreement in the next few months and we will no longer have an involvement in the hotel.
"We would like to take this opportunity to thank Waldorf Astoria and the owners for their support and the combined efforts on both sides to deliver two award winning restaurants - the Pompadour and Galvin Brasserie de Luxe. Special thanks must also go to all the incredible team members who have been a huge part of our Scottish restaurants over the past seven years.
"Our focus will now be towards our current estate and new openings in the year ahead."
Dale MacPhee, general manager of the Waldorf Astoria Edinburgh - The Caledonian said:"The Galvins have contributed a huge amount of energy and enthusiasm to our two restaurant offerings over the past seven years since we became a Waldorf Astoria property. However, our arrangement has come to a natural end this year and both parties reviewed this as an opportunity to pursue new directions.
"It is important to keep our offering fresh and innovative in the competitive Edinburgh restaurant scene and we will have a new operator taking over the Brasserie imminently. As for our fine dining restaurant, The Pompadour, this continues to go from strength to strength under the leadership of Executive Chef, Dan Ashmore and his award-winning team."
Galvin Restaurants now comprises the Michelin-starred Galvin at Windows in the London Hilton on Park Lane hotel, the Michelin-starred Galvin La Chapelle in Spital Square, next door to which is pub Galvin Hop, and Galvin at the Athenaeum hotel in London. In Chelmsford, Essex they have the Galvin Green Man pub, which holds a Michelin Bib Gourmand and two AA rosettes. They also operate Galvin at Centurion Club in St Albans, Hertfordshire, as well as Demoiselle Dubai and Galvin Dubai.
Galvin Restaurants closed Galvin Bistrot de Luxe in Marylebone, in January 2018.Get The Caterer every week on your smartphone, tablet, or even in good old-fashioned hard copy (or all three!).