The story, titled Echo's Bones, was originally commissioned as a final story for 'More Pricks Than Kicks', Beckett's collection of inter-related stories published in 1934.
However, his publisher at the time, Charles Prentice at Chatto & Windus, rejected the story for being far too difficult and strange.
"It is a nightmare...It gives me the jim-jams...Echo's Bones would, I am sure, lose the book a great many readers. People will shudder and be puzzled and confused; and they won't be keen on analysing the shudder. I hate having to say this," he wrote in a letter to Beckett.
It will now be published by Faber & Faber in a new volume edited by Dr Mark Nixon, reader in modern literature at the University of Reading, 'The Observer' reported.
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"The literary merit of Echo's Bones is evident; moreover, it is a vital document," Nixon writes in the introduction of the new volume.
The rejected story features the protagonist of the ninth story, Yellow, published in 'More Pricks Than Kicks'.
In Yellow, the central character, Belacqua, dies after surgery in hospital. In Echo's Bones, Belacqua is faced with an afterlife.
Nixon believes that the failure of the story prompted Beckett, who won the Nobel prize for literature in 1969, to write a poem of the same name, and to use the title again for his first collection of poems, Echo's Bones and Other Precipitates, published in 1935.