The change came after the AEC had urgent talks with the federal government on Friday morning, ahead of the poll on Saturday.
At issue were AEC voting rules for people who tested positive for the virus between last Saturday and before 6pm on Tuesday, who were only going to be allowed to lodge postal votes.
But many missed the deadline for postal vote applications, which closed at 6pm on Wednesday, leaving them without an avenue to cast their ballot.
Phone voting was previously only available to people who tested positive after 6pm on Tuesday.
Now people who tested positive after 6pm last Friday (May 13) will be able to access telephone voting.
The AEC said it acted to resolve the issue after hearing from COVID-positive people who had missed their chance to apply for a postal vote.
"With many jurisdictions internationally not offering voting services for COVID+ voters during the pandemic, we're proud to be delivering the combination of safe and secure voting services for all voters," Electoral Commissioner Tom Rogers said.
Prime Minister Scott Morrison confirmed the change, saying the government had agreed to Mr Rogers' recommendation.
"He's worked through the logistics of all of that and what that means on their call centres, and all those sorts of things," Mr Morrison told Perth radio 6PR.
"We've made it very clear that we would be accepting any recommendations that came forward and this morning, finally, those recommendations have come forward."
A Melbourne independent candidate for the election had threatened to take the federal government to court to ensure people excluded by the postal deadline could instead vote by phone.
Teal contender Monique Ryan, who is running in Treasurer Josh Frydenberg's seat of Kooyong, said she was relieved the government had agreed to change the regulations.
After raising more than $126,000 for the court action, Ms Ryan said she intended to offer a refund on unspent funds to all donors, although some had already indicated they did not want their money back.
"In that event, we will donate any remaining funds to a charitable legal advocacy fund to keep fighting for all Australians' ability to vote," she said.
It is believed more than 200,000 Australians tested positive for COVID-19 between Saturday and Tuesday, some of whom may have already cast their ballot through postal and pre-poll options.
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