The bat, which Bradman used in his first Test in 1928, is expected to fetch up to AU$120,000.
Bradman was dropped after an inauspicious debut in which he scored 18 and one in Australia's 675-run thrashing by England in the first Test in Brisbane in 1928-29.
The entire 1928-29 Australian team as well as the conquering English who won the series 4-1 have signed the bat. Forty-seven signatures in total are on the bat.
Bradman donated the prized bat in 1930 to a competition run by The Sun newspaper in Sydney. The competition was to help raise money to endow the Don Bradman Cot to the Royal Alexandra Hospital for Children.
Sydney youngster George Lethbridge won the competition by selling the most tickets - 20,000 in total.
The bat has remained in the Lethbridge family until now, but son Robert decided that on the 100th anniversary of Bradman's birth on Aug 27, it was the right time to auction it.
It will be offered for sale by Melbourne's Leski Auctions later this month and has a pre-sale estimate of AU$ 90,000 to 120,000.
"This remarkable bat is 'ground zero' of Bradman's Test career," said auctioneer Charles Leski.
Leski said the bat comes with the original certificate given to George Lethbridge, as well as copies of newspaper articles and photographs which appeared during the competition.
These confirm Bradman used the bat in the Brisbane Test match in November 1928.
The bat featured in an Australian Icons exhibition at the NSW State Library in 2006.
The 20-year-old Bradman returned for the third Test of the 1928-29 Ashes series, which Australia also lost, but with innings of 79 and 112.