The discovery of the cap came as a surprise because it was believed that the 1948 touring members received just one cap each and a collector paid 400,000 dollars (310,000 US dollars) for Bradman's other cap last year.
The cap was uncovered in the wardrobe of retired lawyer Kevin Truscott's home in Melbourne and is now in the Bradman Collection at Adelaide's State Library.
When Truscott came forward recently with the second cap, a check of player contracts for the 1948 tour produced by Bradman collection manager Barry Gibbs revealed each player had been given two caps.
Truscott said the cap was given to his father by Bradman in England in 1948.
Bradman, who became a national sporting hero during the 1930s and 1940s when he rewrote cricket's record books, scored 6,996 runs in 52 Tests at an average of 99.94.
He died in his Adelaide home on February 25, 2001, aged 92.
The donation to the Bradman collection was announced at the South Australian Cricket Association's Test match dinner here late Wednesday ahead of the second Test against New Zealand starting at Adelaide Oval on Friday.