The Tale of Kitty-in-Boots was rediscovered by publisher Jo Hanks after she found a reference to it in an out-of-print Potter biography.
Quentin Blake, best known for his work with Roald Dahl, has illustrated the story, to be published in September.
Potter had only completed a single drawing to go with the manuscript.
She sent the story to her publisher in 1914, saying it was about "a well-behaved prime black Kitty cat, who leads rather a double life".
The Tale of Kitty-in-Boots also features an appearance from an "older, slower" version of Peter Rabbit.
Ms Hanks, a publisher at Penguin Random House Children's, found a reference to Potter's letter to her publisher and the unedited manuscript in the 1970s literary history about the author.
Three manuscripts were then found in the Victoria and Albert Museum archive, handwritten in school notebooks - a rough colour sketch of Kitty-in-Boots, a pencil sketch of villain Mr Tod and a dummy book, with some of the manuscript laid out.
Potter said in letters, also kept in the archive, that she had wanted to finish the story but "interruptions began", including the First World War, her marriage and illness.
Ms Hanks said: "The tale really is the best of Beatrix Potter.
"It has double identities, colourful villains and a number of favourite characters from other tales [including Mr Tod, Mrs Tiggy-Winkle, Ribby and Tabitha Twitchit].
"And, most excitingly, our treasured, mischievous Peter Rabbit makes an appearance - albeit older, slower and portlier!"
Once upon a time there was a serious, well-behaved young black cat.
It belonged to a kind old lady who assured me that no other cat could compare with Kitty.
She lived in constant fear that Kitty might be stolen - "I hear there is a shocking fashion for black cat-skin muffs; wherever is Kitty gone to? Kitty! Kitty!"
She called it "Kitty", but Kitty called herself "Miss Catherine St Quintin".
Cheesebox called her "Q", and Winkiepeeps called her "Squintums". They were very common cats. The old lady would have been shocked had she known of the acquaintance.
And she would have been painfully surprised had she ever seen Miss Kitty in a gentleman's Norfolk jacket, and little fur-lined boots.
Now most cats love the moonlight and staying out at nights; it was curious how willingly Miss Kitty went to bed.
And although the wash-house where she slept - locked in - was always very clean, upon some mornings Kitty was let out with a black chin. And on other mornings her tail seemed thicker, and she scratched.
It puzzled me. It was a long time before I guessed there were in fact two black cats!
Ms Hanks said Blake "had to be" the one to illustrate the newly-discovered story.
"It's a challenging brief to illustrate a manuscript written over 100 years ago by one of the world's most beloved authors, but we knew that Quentin's energy, rebelliousness and humour were in keeping with Beatrix's own artistic sensibilities, and therefore exactly what this fantastic book called out for," she added.
Blake said: "It seemed almost incredible when, early in 2015, I was sent the manuscript of a story by Beatrix Potter; one which had lain unpublished for 100 years and which, with the exception of a single drawing, she had never illustrated.
"I liked the story immediately - it's full of incident and mischief and character -and I was fascinated to think that I was being asked to draw pictures for it.
"I have a strange feeling that it might have been waiting for me."
This year marks the 150th anniversary of Potter's birth.  The Tale of Kitty-in-Boots is being published by Frederick Warne & Co, Potter's original publisher.
A new story written by Beatrix Potter more than 100 years ago, featuring Peter Rabbit, is to be published for the first time.