The council, which was led by the Tories in 2017, lent £15m to developers before they fell into administration.
Last year, the local authority – now led by a Labour minority – instructed administrators Teneo to sell the site in an attempt to recoup the millions spent on the project.
Shabina Qayyum, the council leader, revealed on Tuesday that a sale had been agreed, telling BBC Radio Cambridgeshire she was “very glad” a buyer had been found, although she conceded “there has been a loss on the sale”.
The agreed sale price is thought to be in the region of £3m, but the council refused to confirm the figure.
“It is inevitable that the council will need to write off a significant amount of the debt owed. However, we cannot confirm how much until the sale completes,” they said.
“It remains our ambition to see the hotel completed and open as quickly as possible.”
Last month, Ms Qayyum wrote in her column for the Peterborough Telegraph that the council “faces an expected £9m to £13m loss” on the hotel.
Wayne Fitzgerald, the city’s Conservative group leader, said the council was wrong to agree to the sale.
“We disagree with the disposal process,” he said. “The council says it is cutting its losses as it doesn’t want to spend a penny more of taxpayer money on the hotel, but this decision is going to lose the taxpayers millions.
“If a private developer is willing to buy and take the risk, why can’t the council do that? It doesn’t make any sense.”
