She bought the turquoise and gold ring for £152,450 at auction last year, outbidding the Jane Austen's House Museum.
Culture minister Ed Vaizey put an export bar on it until 30 September.
After worldwide donations the museum has since raised enough money to buy the ring and its bid has been accepted.
Contributions to the Bring the Ring Home campaign, set up by the museum in Jane Austen's former home, included an anonymous donation of £100,000 in August.
The museum, in Chawton, Hampshire, was given until December to raise a further £49,000.
Mary Guyatt, curator of the museum, said it had been "stunned by the generosity and light-footedness" of those who had supported the bid.
Mr Vaizey added: "It's clear from the number of people who gave generously to the campaign just how admired Jane Austen remains to this day."
The museum already displays two other pieces of jewellery owned by the writer - a turquoise bracelet and a topaz cross.
The ring is accompanied by papers documenting its history within the author's family.
It passed first to her sister Cassandra, who then gave it to her sister-in-law Eleanor Austen on her engagement to Jane and Cassandra's brother, the Reverend Henry Thomas Austen.
It remained in the family until Clarkson bought it at auction.
The ring will now go on display at the museum in the New Year.
On hearing the museum had been successful in raising funds to purchase the ring, Ms Clarkson said: "The ring is a beautiful national treasure and I am happy to know that so many Jane Austen fans will get to see it at Jane Austen's House Museum."
The museum said it hoped to welcome Ms Clarkson there in the future.
Austen, who lived most of her life in Hampshire, is one of English literature's most celebrated authors.
Fans are celebrating the 200th anniversary of her novel Pride and Prejudice this year.
Although out of copyright and available free on e-readers, it is estimated that Pride and Prejudice sells up to 50,000 copies each year in the UK.

Prof Bryn Hubbard is being honoured for his work as a polar scholar in "glaciology, glacial geology and the structure and motion of ice masses".
Prof Hubbard, who spent nine weeks drilling on the Larsen C ice shelf in Antarctica, will receive the award at a ceremony at Buckingham Palace.
The director of the centre for glaciology at the university said he was "honoured" to be recognised.
The Polar Medal was established in 1904 to reward the participants in Captain Robert F. Scott's first expedition to the Antarctic region.
In recent decades, most awards have been made to scientists who have worked over prolonged periods in harsh conditions to advance knowledge of the polar regions.

The Nuclear Decommissioning Authority (NDA) is overseeing the dismantling of several UK sites, including Dounreay near Thurso in Caithness.
Representatives from the NDA and oil and gas experts have met in Aberdeen to share information.
One of the areas covered was the decommissioning of oil pipelines.
The event was held at Aberdeen's Oil and Gas Technology Centre.
The NDA said it was actively looking outside its sector for technologies to use in the decommissioning of nuclear power sites.
Among major Scottish oil and gas installations being decommissioned are the Buchan Alpha floating production vessel off Aberdeen, and the Beatrice complex in the Moray Firth.
US singer Kelly Clarkson has been thwarted in her bid to take a ring which once belonged to Jane Austen out of the UK.
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An Aberystwyth University glaciologist is to be awarded a Polar Medal.
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The nuclear industry is looking at how it might use technologies being used in the decommissioning of North Sea oil and gas installations.