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Hunt, with whom Jagger had his first child, Karis, told Britain's Guardian newspaper 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.
The Guardian said the 10 letters would be sold by Sotheby's on December 12.
The auction house values the letters from between 70,000 and 100,000 pounds.
Jagger wrote them to Hunt while filming the Tony Richardson movie "Ned Kelly" in Australia.
They are described as showing 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.
"The sale is important," Hunt told The Guardian. "Someone, I hope, will buy those letters as our generation is dying and with us will go the reality of who we were and what life was."
Hunt has said she was the inspiration for the Rolling Stones' song "Brown Sugar," which Jagger wrote while in Australia.
The rock star also cites in the letters the disintegration of his relationship with singer Marianne Faithful, whom he was also dating at the time, and the death of Rolling Stones' guitarist Brian Jones.