The players, who refused to sing their country's national anthem before their first match of the Asian Cup on the Gold Coast, are being kept safe by Australian Federal Police, Prime Minister Anthony Albanese said.
Activists feared the women could face persecution for the silent protest if they returned to their home country after they were branded traitors on Iranian state media.
The Lionesses' team captain Zahra Ghanbari and players Fatemeh Pasandideh, Zahra Sarbali Alishah, Atefeh Ramezanizadeh and Mona Hamoudi had already taken up the government's offer of safe haven, but Mr Albanese said more were welcome.
"If you want our help, help is here and we will provide that," he told reporters in Canberra on Tuesday.
"Australians have been moved by the plight of these brave women. They're safe here and they should feel at home here."
The women gave permission for their names and pictures to be published.
They escaped their Iranian handlers while staying at a hotel on the Gold Coast and were moved to a safe house on Monday night, Home Affairs Minister Tony Burke said.
Conversations about protecting the team started in earnest during the very early hours of Monday morning, he added.
"Once that happened ... it was made clear that there were five women who wanted to be able to stay in Australia," he said earlier on Tuesday.
"They were moved to a safe location by the Australian Federal Police and last night I met with them at that location."
Once the women's applications had been signed off there were celebrations and an outbreak of "Aussie, Aussie, Aussie, oi, oi, oi", Mr Burke said.
"These women are great athletes, great people, and they're going to feel very much at home in Australia."
The rest of the squad were still with their Iranian handlers, he said.
The team's plight prompted the intervention of US President Donald Trump, who had a late-night phone call with Mr Albanese and later congratulated the prime minister for protecting the women.
Mr Trump earlier took to his Truth Social platform to accuse Australia of "making a terrible humanitarian mistake" by allowing the women to be forced back to Iran.
But shortly after the phone call, he did an about-face and praised the prime minister's work in handling the "rather delicate" situation.
"He's on it! Five have already been taken care of, and the rest are on their way," Mr Trump said.
"Some, however, feel they must go back because they are worried about the safety of their families, including threats to those family members if they don't return."
Advocates had been imploring Australian officials to meet with the team to secure their safety after members were seen making what appeared to be an SOS hand signal on Sunday night after their final Asian Cup match.
