From 1952 to 1963, Britain detonated bombs at Maralinga and Emu Field in South Australia, and the Montebello Islands off Western Australia.
Although the sites were remote, many Aboriginal people were forced to move.
Those who remained were exposed to high levels of radiation, which was later linked to significant health problems.
They will now be eligible for a war veterans' Gold Card, which covers most medical costs, Veterans' Affairs Minister Dan Tehan said.
"The measure will provide Gold Cards to indigenous people present at or near Maralinga, Emu Field or the Montebello Islands at the time of the British nuclear tests in the 1950s or 1960s," he said.
Soldiers turn their their backs on a nuclear test at Maralinga
It follows a royal commission - Australia's highest form of inquiry - in the 1980s, and decades of campaigning by survivors and advocates.
The nuclear tests were conducted with support from the Australian government.
The new healthcare subsidy will form part of a A$133m ( £76m, $98m) investment in Australia's federal budget, which will be unveiled on Tuesday.