The year-long oral history project - The Incredible Journey - will cost £90,000 and is supported by the Heritage Lottery Fund and members of the ss Great Britain Trust.
The ss Great Britain's director, Matthew Tanner MBE said: "Brunel's ss Great Britain is one of the world's most important historic ships.
"She could so easily have remained in the Falkland Islands, abandoned and breaking up in Sparrow Cove."
'Memory boxes'
Memory boxes are situated around Bristol
Memory boxes have been placed at libraries and other public buildings across the city - including the reception at the BBC on Whiteladies Road - and there will even be one in the Falkland Islands.
You can write your memory on one of the postcards provided and place it in a box, or e-mail
salvage@ssgreatbritain.org
Rhian Tritton, the ss Great Britain Trust's director of museum and educational services said: "This project gives us a wonderful opportunity to gather the fascinating stories of people involved in the ss Great Britain's epic salvage.
"These memories will play a key part in the ship's 40th anniversary celebrations in 2010."
Callers to BBC Radio Bristol's The Interactive on Friday shared their memories with presenter Phil Gayle.
Amy and her late husband stood next to Spike Island. "It was marvellous," she said.
"I looked at my husband and said to him, whatever are they going to do with that, scrap it? He said no, I believe they're going to repair it..."
While on a cruise in the mid-Atlantic in 1970, Diana and the other passengers on the Southern Cross heard an announcement from the captain to go to the starboard side of the ship to see the ss Great Britain passing.
"I think I must have been one of the first Bristolians to see it," she told Phil.
Ray was in his late teens when the ss Great Britain returned. He was aboard one of the tugs which brought the ship into Avonmouth and then up the Avon itself on July 19.
"You can't describe the feeling - it was absolutely magic, it really was tremendous."
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