The cap, bought from a private owner, is one of 11 worn by Bradman known to exist.
One that he used during India’s 1947-48 tour of Australia, his final test series on home soil, fetched US$250,000 last year.
Australia’s cricketers are awarded the dark green woollen caps before test debuts and they are revered by players and fans alike.
Arts Minister Tony Burke said the purchase safeguarded an important piece of national history.
“You’d be hard-pressed to meet an Australian that hasn’t heard of the great Donald Bradman, arguably the greatest cricketer of all time,” he said.
“Now to have one of his iconic baggy greens in the National Museum of Australia means visitors will have the opportunity to get up close and connect with our sporting and cultural history.”
The cap will go into the National Historical Collection in Canberra alongside other Bradman memorabilia, including an autographed bat from the first test at Trent Bridge in Nottingham during the 1934 Ashes series.
Bradman, described by cricket authority Wisden as the greatest to “have ever graced the gentleman’s game”, died in 2001 aged 92.
– Agence France-Presse