The man and woman, aged in their late 30s to early 40s, were from the London area and their bodies were discovered at the Majestic Hotel and Spa, part of the Doubletree by Hilton chain, at 10.20pm on Tuesday May 4.
The deceased were known to each other and nobody else is being sought in connection with their deaths.
The Majestic Hotel dates back to 1900 and attracted European and Indian royalty during its heyday. It has survived two major fires and was taken over by Hilton and rebranded in 2016.
Detective Superintendent Wayne Fox of North Yorkshire Police’s Major Investigation Team said: “We were called at around 10.20pm on Tuesday May 4 by staff at the Majestic Hotel to a report that the bodies of a man and a woman had been located in a hotel room.
“On arrival, a man and a woman, both in their late 30s/early 40s from the London area, were pronounced dead at the scene by colleagues from the ambulance service. Their families have been informed and are being supported by specially-trained officers.
“A detailed investigation is under way looking into the circumstances of both deaths. We can confirm that we are not looking for anyone else in connection with the deaths and would like to reassure the local community that we believe that this is an isolated incident.”