The 81-room, four-star venue will feature a 150-cover Steakhouse Bar & Grill from celebrity chef Marco Pierre White.
It is set to create up to 60 new jobs when it opens in autumn 2017.
Property developers Kevin Brown and Shaun Crawley have completed the deal with Maven Capital Partners, and will lead the renovation on behalf of the company.
Brown said: “Tourism plays a significant part in Durham’s economy, but there is a widely recognised shortage of quality hotel accommodation.
“On completion, the new hotel should attract up to 21,000 new visitors to the city annually.”
Originally built in 1896 as the headquarters for Durham County Council, Shire Hall features grand tiled marble staircases, stained glass windows, and a circular debating chamber that will be transformed in to White’s restaurant.
It is the chef’s third restaurant to open in a Maven Capital hotel, following sites in Glasgow and Cardiff.
Nick Taplin, chief executive of Black & White Hospitality, which owns the franchise rights to MPW Steakhouse Bar & Grill, said: “Marco and I have been eager to find a suitable location in the city for some time.
“We know that Durham has a real appetite for affordable glamour and restaurants that offer top quality dishes in a sumptuous environment, at a price to suit all budgets.”
The refurbishment of the hotel is expected to take 15 months.