"Yes, Australia has granted her asylum, but we are waiting to hear where exactly she is going," immigration police chief Surachate Hakparn told CNN.
Hakparn said Canada had also offered Rahaf Mohammed al-Qunun asylum and they were waiting for her decision.
The UN refugee agency UNHCR had referred Qunun's protection request to Australia on Wednesday, though it had not been confirmed before now that Canada was also considering her case.
Hakparn said Qunun, who is staying in an undisclosed location in Bangkok, would be leaving Thailand "almost as soon as the final decision is made".
"We are providing necessary security for her," he told CNN.
The Australian Department of Home Affairs has not commented on the development.
Qunun had flown to Thailand from Kuwait to escape her family, saying she feared they would kill her because she renounced Islam.
She intended to fly on to Australia but barricaded herself in a hotel room in the Bangkok airport on Sunday after Thai immigration officials attempted to deport her back to the Middle East.
Qunun and her supporters drew global attention to her case through a social media campaign launched mostly on Twitter.
She documented her arrival and subsequent detention in Bangkok on her smartphone, creating new Twitter and Periscope accounts where she received a deluge of supportive messages.
Her story has also put Saudi Arabia's guardianship laws, which restrict many aspects of women's lives, back under international scrutiny.
In response to the media campaign, Thai authorities allowed her access to the UNHCR and did not deport her to Kuwait.
On Friday, Qunun's Twitter account appeared to have been deleted.