The infamous balloon was donated to the National Gallery of Australia anonymously, the gallery said in its 2018-19 annual report.

The donation was made several months ago through the Cultural Gifts Program,which offers tax incentives to encourage people to donate cultural items to public art galleries, museums, libraries and archives in Australia.

It's a fitting return, given the balloon first took to the skies from outside the gallery more than six years ago.

National Gallery director Nick Mitzevich said it was a long-awaited homecoming.

"This artwork is one of the most talked about artworks in the history of Australia," Mr Mitzevich said.

"I love the fact people have an opinion about it, and you don't have to go to a gallery to see it."

The acquisition is part of a bigger plan for the gallery, which Mr Mitzevich is keeping a lid on for now.

"I was keeping it quiet for a little bit longer, because it's part of something even more exciting which I can't tell you about today," Mr Mitzevich said.

"This is just one part of something even bigger we're working on to reveal on November 20."

The so-called "Hindenboob" was commissioned by the ACT government to mark the centenary of Canberra in 2013.

Former Canberra artist Patricia Piccinini said the creature was inspired by the planned nature of the national capital.

"My question is what if evolution went a different way and instead of going back into the sea, from which they came originally, they went into the air and we evolved a nature that could fly instead of swim," Piccinini said at the time.

But it attracted much controversy over its unusual design and $300,000-plus pricetag.

Even former chief minister Jon Stanhope - who himself was criticised for signing off on a $400,000 fibreglass owl to be installed in Belconnen - said the balloon had "embarrassed" the ACT government.

But then chief minister Katy Gallagher said the cost was minor compared to the entire budget for the centenary.

The government spent $24.5 million on commissioning a range of centenary events, including $500,000 on an international one-day cricket match, $300,000 on fireworks and $160,000 each on Canberra Symphony and ballet performances.

Skywhale attracted more publicity than all of them.

International news agencies, from the UK to Lebanon to Venezuela, ran photos and videos of the balloon in flight over Canberra.

"Controversy over giant turtle with breasts," read one French headline.

Since the balloon left Canberra, it has drawn huge crowds overseas.

It has featured at the Trans Art Tokyo festival, Ireland's Galway Arts Festival and has had lengthy displays in the Brazilian cities of Sao Paulo and Rio De Janeiro.

The balloon returned to Australia at some point in the past two years. It floated above the Yarra late last year and most recently featured at the Hunter Valley Night Glow in April.

But Piccinini said it was her "dream" that Skywhale would return to Canberra.

"The Skywhale is all about Canberra. She was born there," she said in 2017.

"My dream is for her to come back one day and fly over Lake Burley Griffin."

Global Ballooning - the company that owned Skywhale - also said it wanted to bring her back to her natural habitat.

"The short answer is we love ballooning in Canberra and given the Skywhale is still flying - we just await an invitation and someone with a budget," director Kiff Saunders said in 2016.

The balloon will fly at the Canberra Balloon Festival next March before touring around the country as part of a travelling exhibition.

"What's brilliant about Skywhale is we don't need to go to towns and cities that have galleries," Mr Mitzevich said.

"All we need is a vacant field, good weather conditions and an excited community."

But Canberrans may see it sooner, Mr Mitzevich hinted.

"What I will say is Canberrans should keep their eagle eyes on the sky," Mr Mitzevich said.