The Iranian asylum seeker was killed during a riot in the Papua New Guinea-based detention centre in February.
A government report handed down three months later found that a PNG man employed by The Salvation Army led the beating that killed the 23-year-old.
Mr Burnside said he had received a sworn statement from an eyewitness detailing the fatal attack.
Listen: Julian Burnside speaks with Ron Sutton about winning the Sydney Peace Prize.
“An employee of the detention centre, armed with a length of timber with two nails driven through it, had lashed out at Reza Berati and had brought down two crushing blows on his head,” he said.
“He fell to the ground and was then kicked repeatedly鈥?Then another employee of the detention centre got a rock and brought it down on Reza Berati鈥檚 head with such ferocity that it killed him.”
Accepting the Sydney Peace Prize on Wednesday night, the human rights lawyer condemned the length of time it took for people to be charged over the death, alleging that detainees had been offered transfers to Australia in response for silence.
“It is my understanding that some people in the Manus Island detention centre are being offered the opportunity of being taken to mainland Australia on the condition that they withdraw any witness statements they鈥檝e made,” he said.
Immigration Minister Scott Morrison has dismissed the claim as false.
In a statement to SBS, Mr Morrison called the allegation offensive.
鈥淭his is a false and offensive suggestion made without any basis or substantiation by advocates with proven form of political malice and opposition to the Government’s successful border protection policies,” he said.
“The government once again rejects these claims.鈥?/p>Asylum seekers 鈥榤istreated in every possible way鈥?/strong>
Mr Burnside said there were many injustices in Australia, but asylum seekers arriving by boat were “mistreated in every possible way”.
“It is one of the great and wilful injustices in our society which runs like a poison through the Australian politics,” he said.
“We鈥檝e known for years that refugees, fleeing persecution, risk their lives to get to safety here. We have known for years that those people are locked up, regardless of the fact that they鈥檝e committed no offence.”
Mr Burnside described the 2013 federal election as a low point in the country鈥檚 record of human rights.
“It is only time in Australia鈥檚 political history when both major political parties have courted political favour by promising cruelty to a particular group of human beings,” he said.
鈥淚t is probably the most shameful moment in Australia鈥檚 political history.鈥?/p>Whitlam was 鈥榓 colossus鈥?/strong>
Mr Burnside also spoke on Wednesday鈥檚 memorial service for the late Gough Whitlam, saying that he admired the former prime minister.
He described Mr Whitlam as 鈥渁 colossus鈥?before moving on to condemn the lack of women represented in parliament.
鈥淚f the position were reversed and women held most of the positions in politics, the cries of injustice would be immediate and deafening,鈥?he said.
鈥淏ut look at the makeup of the current federal cabinet and note how it is defended against criticism.鈥?/p>