Home Affairs Minister Tony Burke said a player and a support staff member accepted the government's offer, after five players from the team were granted asylum a day earlier.
"I made them the same offer that I made the five players the night before," Burke told reporters.
"If they wanted to receive a humanitarian visa for Australia, which would have a pathway to a permanent visa, I had the paperwork ready to execute that immediately."
Australian officials talked to most members of the team separately at Sydney airport and were informed of their options before they flew out of Australia.
"What we made sure of was that there was no rushing, there was no pressure. Everything was about ensuring the dignity for those individuals to make a choice," Burke said during a media briefing in Canberra.
Some discussed their options with family but they declined the offer to remain in Australia. The team has reached Kuala Lumpur on their way to Iran.
Concerns about the players' safety grew after Iranian state television labelled the team "wartime traitors" for refusing to sing the national anthem during an Asia Cup match in Australia.
The Iranian team's campaign in the tournament started just as the U.S. and Israel launched air strikes on Iran, killing the Islamic Republic's Supreme Leader Ayatollah Ali Khamenei. They were eliminated from the tournament on Sunday.
A group of Iranians living in Australia gathered to protest against the Iranian government and surrounded the players' bus in Gold Coast when they left the hotel for the airport.
Many also turned up at the Sydney airport on Tuesday evening while they were being transferred to the international terminal, television footage showed.
The office of Iran's general prosecutor said on Tuesday the remaining members of the team were invited back to the country "with peace and confidence," Iranian media reported.