Australian artist Lindy Lee's Ouroboros is to be a 13 tonne, four-metre-high torus of reflective recycled metal which will be installed in the gallery's garden in 2024.

Lee said the work was "symbolic of repetition and renewal, of the abundance of cyclical time, eternal flow, unity of the beginning and the end, transformation and alchemy".

In a statement, she said she wanted the work to become "a beacon" for visitors and passersby, "pulsing with light and energy".

"During the day its highly polished mirror surface will reflect the imagery of the floating world - the transience of passers-by, cars, birds in flight, and stunning clouds," she said.

"And at night the Ouroboros will be lit internally, returning its light to the world."

The National Gallery's last most expensive purchase was James Turrell's skyspace Within without for $8.2 million in 2010.

Adjusted for inflation, the most expensive purchase this century was Lucian Freud's oil painting After Cezanne, bought for $7.9 million in 2001.

The cost and size of the commission is reflective of current director Nick Mitzevich's new collecting policy, which he has said aims to make the national collection "better and smaller", with a focus on fewer, more significant acquisitions.

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"Art's such an important part of the cultural fabric of our city, or community and our country and we continue to do that job, even remotely," he said on Thursday.

"In some ways it's emblematic of the fact that the gallery has always been ambitious in what it's done."

He said the gallery considered Lindy Lee to be "at the top of her game", based on a long track record of work and international commissions.

"Lindy was asked to be bold and ambitious in her vision for this project and she has exceeded our expectations," he said.

"We're looking forward to welcoming hundreds of thousands of people to enjoy the work once it's finished."

The work will sit at the gallery's main entrance, and will be accessible day and night.

People will be able to walk into the mouth of the sculpture and enjoy it from within, Mr Mitzevich said.

It's the first commission for the Sculpture Garden since the opening of James Turrell's skyspace Within without in 2010.

The project's next milestone will be seeking National Capital Authority approval for the works, which will begin this month. The work is due to be completed in early 2024.

The sculpture will reference the ouroboros, a mythical snake eating its tail.

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