Barnard allegedly bragged about the murder to amnesty applicant Kevin Trytsman, 28, of Sandton while the latter was awaiting trial on charges of illegal possession of firearms and ammunition, and vehicle theft.
Trytsman, who claimed he had been storing the weapons on behalf of Umkhonto we Sizwe, told the committee Barnard and Military Intelligence agent Eugene Riley had approached him in prison seeking information about his MK commander.
He had become friendly with the two and Barnard had admitted to being Webster's assassin and that Riley had driven the getaway vehicle.
Trytsman said he was called to give evidence at the inquest into Webster's death but had failed to tell the inquest of Barnard's statement.
Testifying before the Truth Commission's human rights violations committee in Johannesburg last year, Webster's former partner Maggie Friedman implicated five other CCB operatives in the murder - Wouter Basson, Staal Burger, Chappie Maree, Calla Botha and Slang van Zyl.
Webster, a social anthropology lecturer at the University of the Witwatersrand, was shot dead by gunmen in a passing car outside his Troyeville, Johannesburg home when he and Friedman returned home from walking their dogs.
Friedman told the commission: "I heard something like a car backfiring. I realised something was wrong when I saw David clutching his chest. He said `I've been shot by a shotgun. Get an ambulance.
"He fell down on the pavement and died about half an hour later."
The academic played a prominent role in various anti-apartheid organisations such as the End Conscription Campaign, Detainees' Parents' Support Committee and the Five Freedoms Forum.
Although his murder was the subject of at least seven investigations - including the Harms Commission of Inquiry and an internal military inquiry - no-one has ever been prosecuted.
Trytsman, who did not appear at a public hearing of the amnesty committee, was granted amnesty for the illegal possession of firearms and ammunition, vehicle theft and perjury.
In his amnesty application he said he was found in possession of an AK-47 rifle, two magazines and a car on a farm he was renting near Knoppieslaagte.
He was given a suspended sentence for possession of the firearm, a fine for the possession of the magazines and a five-year jail sentence for vehicle theft.
He told the committee he had given the court false explanations for possessing the material, concealing the fact that he had been storing them on behalf of MK. Trytsman was sentenced in 1994.