The property, operated under Brownsword's Abode brand and described as England's oldest hotel, was evacuated early on Friday as a precaution after the fire, which broke out in Castle Fine Art gallery on Cathedral Green, started to spread into neighbouring buildings.
It continued through to the 53-bedroom hotel, leading to the collapse of the building's facade the following morning.
While fortunately all guests and staff were safe, Brownsword said the loss of the building was 'heart-breaking'.
In a statement he said: "Alongside many of Exeter’s residents and visitors, we share a huge sense of loss of such an iconic building, and remember fondly our memories of happy times there.
"Amidst the tragedy, I have been reminded of the commitment, professionalism and dedication of so many people, and I would like to thank everyone for their overwhelming support."
Brownsword praised the hotel's general manager John Badley and his team for ensuring all guests and staff were evacuated safely and for their ongoing help to guests.
"I am extremely proud of all the team," he said. "I would also like to thank the city of Exeter and the many, many people who have helped us since the events of Friday. We are so grateful for the incredible efforts of the emergency services, especially the fire service who attended in huge numbers to assist in the effort to save The Royal Clarence and surrounding buildings."
"We’d also like to extend our thanks especially to the Council and to The Mercure Southgate Hotel, who offered every assistance to help both our staff and guests including refuge and temporary office space."
Brownsword said the company, which operates 13 hotels across the UK, said 'every intention' to rebuilt Abode Exeter with 'enormous sympathy to its importance and heritage'.
"We have always said we believe we are merely custodians of the buildings our hotels operate within, and we pledge to do our very best to return The Royal Clarence to the city of Exeter and its people," he said.
The Royal Clarence hotel was built in 1769 as The Assembly Rooms. It was co-owned by Brownsword and Michael Caines between 2000 and 2015. Brownsword bought the hotel in 2003 for £4.5m.
It is not yet known the extent of the financial damage or when building work will start.