Dennis "Tink" Bell, 25, died after falling down a crevasse on a glacier at Admiralty Bay on King George Island in 1959.
A team from the Henryk Arctowski Polish Antarctic Station found his remains among rocks exposed by a receding glacier in January this year, the BAS said on Monday.
Bone fragments were carried to the Falkland Islands on the BAS Royal Research Ship Sir David Attenborough and handed to the coroner for British Antarctic Territory Malcolm Simmons, who brought them back to London from Stanley.
DNA testing carried out at King's College London finally matched the remains with samples from Bell's brother David and his sister Valerie Kelly.
"When my sister Valerie and I were notified that our brother Dennis had been found after 66 years, we were shocked and amazed," David Bell, now living in Australia, said.
Bell trained as a radio operator in the Royal Air Force before joining the Falkland Islands Dependencies Survey as a meteorologist in 1958.
He was stationed for a two-year assignment at Admiralty Bay, a small UK base with half a dozen men, on King George Island - one of the South Shetland Islands which lie in the Southern Ocean about 200 kilometres off the northern coast of the Antarctic Peninsula.
On July 26, 1959, Bell and three of his colleagues - meteorologist Ken Gibson, surveyor Jeff Stokes, and geologist Colin Barton - left base with two dog sleds to climb the glacier and carry out a survey and geological work.
But on the way up, the soft snow made the journey difficult, and the dogs began to show signs of tiredness.
"To encourage them, Bell went ahead... tragically without his skis," the BAS said.
"Suddenly, he disappeared, leaving a gaping hole in the crevasse bridge through which he had fallen."
According to accounts in the British Antarctic Survey records, Stokes made a first attempt at lifting Bell out of the hole using a rope.
But Bell had tied the rope around his belt, which broke as he reached the lip of the crevasse.
After this second fall, Bell no longer responded to calls from Stokes.
"That's a story I shall never get over," Bell's brother David told the BBC.
Stokes later met with Gibson and Barton coming down the glacier, and the three men made another attempt at finding Bell.
But weather conditions rapidly deteriorated, and they were not able to reach the crevasse in time, according to the BAS records.
"It was probably 12 hours before we found the site and there was no way he could have survived," Gibson said.
Dennis was the oldest of three siblings.
"(He) was my hero as he seemed to be able to turn his hand to anything, servicing petrol engines, photography including processing his own films," his brother said.
Dennis was remembered warmly in reports from the station, the BAS said.
"He's cheerful and industrious, with a mischievous sense of humour and fondness for practical jokes," the BAS said on Instagram.
He was described as the best cook in the hut and was known for raising two litters of the husky dogs used to pull sleds.
The Polish expedition, which recovered Bell's remains, also found over 200 personal items, including the remains of radio equipment, a flashlight, ski poles, an inscribed Erguel wristwatch, a Swedish Mora knife and ski poles.
