SSP Shalabh Mathur told media that "it appears the two were dead Monday night itself, as the food they had ordered had not been eaten".
The British High Commission was informed Tuesday morning.
Police said the two was identified as James Oliver, 28, and Alexendra Nichola Gaskel, 24, from their passports.
The two had come to India July 11. They came to Agra Oct 18 and put up at the Residency Hotel. They shifted to Hotel Maya, close to the Taj Mahal, Oct 20.
The hotel staff informed the police Tuesday morning when there was no response from their room.
The bodies were sent to S.N. Medical College for post-mortem examination.
Mathur said the cause of their death will be established once the report arrives. Police had found stress-relieving drugs and sleeping pills from the room.