Mr Gandy deposited Mr Turing's papers at the Archive Centre at King's College in Cambridge in 1977.
But Mr Gandy retained the 56-page notebook because of a deeply personal message written in the blank centre pages of the notebook which he wanted to keep private.
The notes remained hidden among personal effects until after his death.
Scholar Andrew Hodges, said: "Alan Turing was parsimonious with his words and everything from his pen has special value.
"This notebook shines extra light on how, even when he was enmeshed in great world events, he remained committed to free-thinking work in pure mathematics."
Mr Turing committed suicide in 1954 as a consequence of hormone treatment to "cure" his homosexuality which he was undergoing as an alternative to imprisonment.
The story of his life was told in the 2014 Oscar-winning film The Imitation Game.