The 10 letters, dating from the summer of 1969, had been expected to fetch 70-100,000 pounds, according to the auctioneer.
"The passage of time has given these letters a place in our cultural history," Hunt said after the London sale.
"1969 saw the ebbing of a crucial, revolutionary era, highly influenced by such artists as The Beatles, The Rolling Stones, James Brown and Bob Dylan.
"Their inner thoughts should not be the property of only their families, but the public at large, to reveal who these influential artists were - not as commercial images, but their private selves."
Hunt, with whom Jagger had his first child, Karis, told Britain's Guardian newspaper last month that she was selling the letters, written in July and August 1969, because she had been unable to pay her bills.
"I'm broke," Hunt, who lives in France, told the newspaper.
Jagger wrote them to Hunt while filming the Tony Richardson movie "Ned Kelly" in Australia.
They showed a sensitive side of the then-young singer, who wrote about the poetry of Emily Dickinson, meeting author Christopher Isherwood and an unrealized multimedia project.
Jagger's relationship with Hunt, who is African-American, was kept under wraps until 1972.
Hunt has said she was the inspiration for Brown Sugar, which Jagger wrote while in Australia.
The rock star also cites in the letters the disintegration of his relationship with singer Marianne Faithfull, whom he was also dating at the time, and the death of Rolling Stones' guitarist Brian Jones.
There has been a surge in interest in the rock band this year, as Jagger and his three surviving bandmates celebrate the 50th anniversary of the Stones with a series of concerts, a photo book and a greatest hits album.
(Reporting by Mike Collett-White)
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