Jocelyn Elliott, 76, was released over the weekend after three weeks in captivity.
She and her husband Ken, 81, who is still a hostage, had provided services in the town of Djibo since the 1970s.
Militants reportedly said the kidnapping was an attempt to secure the release of imprisoned fighters.
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Mrs Elliott arrived in Burkina Faso's capital, Ouagadougou, where she met president Roch Marc Christian Kabore, on Monday.
"I really hope to be with my husband soon so that we can again go to Djibo and continue (our work) there," she told journalists.
She said she was happy to be with her "Burkina family" and thanked the governments of Niger, Burkina Faso and Australia, but gave no details of her captivity or release.
The aid worker was freed in neighbouring Niger after the jihadists from the group al-Qaeda in the Islamic Maghreb (AQIM) said they did not want "to make women involved in the war".
Niger acted as a mediator to secure her release, officials said.
The couple were kidnapped in Djibo, near the border with Mali, on the same day as a deadly attack on a hotel in Ouagadougou, which was also claimed by AQIM.
Burkina Faso's Foreign Minister, Alpha Barry, told the AFP news agency that "no ransom was paid or conditions imposed" by the kidnappers for her release.
Efforts to free Mrs Elliott's husband were continuing, he said.
In response to their abduction, local people in Djibo launched a social media campaign calling for their release.
An Australian aid worker who was freed by al-Qaeda-linked militants in Burkina Faso has vowed to continue with her medical charity in the country.