Heger tore them up in shock, but they were retrieved from a rubbish bin by his wife who sewed them back together and preserved them.
One, composed in French, reads: "If my master withdraws his friendship from me entirely, I shall be absolutely without hope."
Another, with a postscript written in English, reads: "I must say one word to you in English - I wish I would write to you more cheerful letters, for when I read this over, I find it to be somewhat gloomy - but forgive me my dear master - do not be irritated at my sadness - according to the words of the Bible: 'Out of the fullness of the heart, the mouth speaketh', and truly I find it difficult to be cheerful so long as I think I shall never see you more."
The letter was written in 1844, two years after Bronte, then age 28, met Heger, her tutor, and three years before the publication of Jane Eyre, her first major work.
The story echoes the plot of her 1853 novel Villette, about a young women with an unrequited love for her Belgian teacher.
By the time Heger was shown the letters by his daughter on his death bed, Bronte had died age 38 and was a recognised writer. The family decided to keep the correspondence, but the writer's love for Heger was tactfully omited from a biography written by her friend, Elizabeth Gaskell.
Rachel Foss, of the British Library, said: "Having been burnt, sold, cut up and destroyed, it is remarkable that these letters have survived.
"Seeing the torn-up letters with the careful stitches holding them together is remarkably evocative and moving. You get a really vivid sense that they have a story to tell."
Love Letters: 2000 Years of Romance, is published by the British Library and features correspondence from Oscar Wilde, Henry VIII, Rupert Brooke and Lord Nelson.