Four of the supersonic jets which were retired last Friday will be kept in UK, with two going to the United States and one to Barbados in West Indies.
The airline said it had set up a study with Airbus to see whether a single Concorde could be kept useable for non-commercial events such as fly-pasts and air shows.
But the study has ended hopes of Concorde fans.
"A detailed study with Airbus has regrettably led us both to conclude that it would not be possible," British Airways chief executive Rod Eddington said.
The decision is a bitter disappointment to fans of the plane, who turned out in their thousands last week to watch the final three passenger-carrying Concorde take to the skies for the final time.
"So the dream is over, Concorde's future indeed is solely as an exhibit in museums in the UK and overseas," mourned a fan.
"So the dream is over, Concorde's future indeed is solely as an exhibit in museums in the UK and overseas"
"I hope Airbus rot and go bust," said a more bitter fan.
Eddington said the final resting places of the seven Concordes have been chosen with care.
"We have chosen the final homes based on a number of criteria: their ability to properly exhibit and preserve the aircraft, their geographical location and accessibility to the public," he said.
The airline also announced it would hold a charity auction on 1 December to sell off a series of Concorde spare parts, including a nose cone, a pilot's seat and one of the in-cabin devices which indicated the plane's speed.
The Concordes have been retired due to falling passenger numbers and spiraling maintenance costs.