The site has been bought by regional development agency One NorthEast which plans a mix of cafes, bars and new homes around an urban square.
The decision was narrowly approved by a 10-9 vote at a private session of the full council on Thursday night.
However, it led to a scathing attack on the council from Coun John Robertson who has tendered his resignation from the controlling Liberal Democrat group.
"At the moment the leadership at the top is non-existent and I have no wish to be part of it," said Coun Robertson, who also announced his resignation as chairman of the town's Chamber of Trade so he could speak during the debate without declaring an interest.
He added: "The easy option is selling the car park rather than hold on and wait for the result of a traffic management survey that has just been commissioned and doesn't report back until October.
"What happens if that report comes back saying how valuable that car park is to the bottom end of town?"
While the purchase price has not been disclosed, it is understood the council is planning to put the proceeds towards its £320,000 commitment to the proposed £5.1 million redevelopment of the Dewar's Lane granary.
"Someone has offered them money and they've realised that money will help meet existing commitments at the granary so therefore we are giving up a strategically important car park to underpin the granary project," explained Coun Robertson.
One of Berwick's biggest employers has already warned that plans to sell the Quayside car park could have disastrous consequences.
Chartered accountants Greaves, West and Ayre, which employs around 100 people in Berwick, had written to the council expressing its concerns and even warned it could force them out of the town centre.
Tim Kirton, Berwick Borough Council's head of regeneration, responded: "The (parking and traffic management) strategy should include the identification of actions to mitigate the effects of any loss of parking spaces through future development at the Quayside.
"However, the strategy is not limited simply to finding alternative vehicle parking spaces and will consider all options including the possibilities and viabilities of encouraging walking, cycling, bus services and park and ride.
"The mere provision of more car parking spaces can actually add to congestion problems by encouraging ever more vehicles into the town centre, creating gridlock.
"The streetscape of Berwick was laid out in medieval times and the town is simply not designed to accept endlessly increasing numbers of cars, indeed it is close to choking point now."
The subject had been deferred at the May meeting of full council when Coun Robertson sought assurances that One NorthEast would not redevelop the car parking before alternative parking was found.
"We still have no assurances," said Coun Robertson. "We have got the car park for one year- after that point there are no guarantees.
"With the best will in the world it is going to take longer than that to set up a park and ride scheme or find alternative spaces.
"They are threatening the livelihood of business and residents at the bottom end of town, particularly when you consider the extra flats and accommodation the planning committee has recently passed which is going to create even more parking demand in that part of town."
Kim Kirby, chairman of the Bridge Street Traders Association, added: "The parking situation is already pretty serious and if the council take away the Quayside car park it will be bad news for business here."
The Quayside is one of 10 priority sites identified in the Berwick masterplan, also known as the Berwick's Future initiative, which is designed to kickstart economic and social regeneration in the town.It is acknowledged the Quayside area is vastly underused at the moment so the aim is to try and recreate the bustle of a busy waterfront.