The government has brought forward the release of the places by two months after political pressure.
The spots were originally going to be rolled out from the start of November, but will now be made available between between September and the end of October.
Labor's political backflip follows revelations more than 200,000 people were on the waitlist for a home care place, with one Australian dying every two hours while waiting for the care they need.
The opposition, Greens and independents seized on the figures, urging the government to release more packages sooner.
Aged Care Minister Sam Rae said the decision to free up 20,000 places would give certainty to older Australians and the industry.
"These reforms are about reshaping aged care so it delivers more care sooner and closer to home," he told parliament on Thursday.
Aged care providers have welcomed the legislation's passage.
"Bipartisan support in politics is as rare as the Tasmanian tiger, but the looming introduction of the new aged care act is a wonderful example of politicians putting older Australians ahead of politics," Ageing Australia chief executive Tom Symondson said.
Opposition Leader Sussan Ley said she would keep up pressure on the government to make sure it delivers the promised 20,000 packages before the end of October.
"The coalition will continue to fight for older Australians with one clear goal: no-one should have to wait for the care they have been assessed as needing," she told parliament.
"This is a moment where an arrogant government has been brought to heel... Labor has been forced into a humiliating backdown."
Another 20,000 home care spots will be released in November and December and 43,000 more will be rolled out in the first half of next year.
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