The group will use online bidding software from Australian based provider Live Global Bid when the test captain's cap along with other historic sporting items go up for bids in Sydney on 30 September.
Bradman's baggy green from the 1946-47 series against the touring England side is touted as the highlight of the auction, estimated to fetch somewhere between AU$300,000-AU$500,000.
Other items up for grabs include the England cap worn by Eric Hollies after he bowled Bradman for a duck in the final inning of the legend's Test career in 1948, with an estimated sell price of AU$40,000-AU$60,000.
Lawson Menzies marketing manager, Lisa Tycehurst, said the Internet has provided the group "a new distribution channel that has not been available to us before".
The centenary cap presented to Mark Waugh by Prime Minister John Howard in 2000 will also be auctioned off, as well as the Australian batsman's helmet, bat, gloves, pads and shirts.
Other high profile items is the official catalogue of yearlings sold in 1928 in New Zealand, among which is the legendary race horse Phar Lap. The silks and cap of jockey Jim Cassidy is also available, from his triumphant ride on Might & Power in the 1997 Melbourne Cup.
The auction is accessible at the Web site www.lawsonmenzies.com.au to registered Internet bidders. Viewing of the items is available on the 25th, 26th, 27th and 29th of September.