The edition of The Cuckoo's Calling was given by the author to friend Margaret Darling to help with fundraising efforts for the charity EdUKaid, which works with children, their families and schools in rural Tanzania.
The crime novel about the murder of a fictional supermodel, which was published earlier this year, will be sold at Sotheby's, London.
It was published under the false name but Ms Rowling was later unmasked as the true author after one of the partners at her law firm told a friend, who divulged it on Twitter.
Ms Darling said: "Jo knows the value of education. She was a teacher. Her very special gift will allow EdUKaid and the community to put desks, water, sanitation, blackboards into schools like Mnaida."