The book, published in 1885 by the author of the classic Treasure Island, was given to the Oxfam shop in Glasgow's Byres Road.
The copy of A Child's Garden Of Verses was a gift from Stevenson's mother to her niece and nephew.
It comes with the inscription "To my GG Niece and Nephew at Chudleigh with kind love."
The money from the sale at Bonhams will be used to fund future Oxfam projects.
Shop manager John Connolly said: "Donations like this are rare and we are delighted with this sale."