Alan Turing was given a posthumous royal pardon, in 2013, prompted by a campaign led by former MP John Leech.
One of the documents shows the mathematician admitted “acts of gross indecency” at a trial in 1952, before he underwent chemical castration.
He was arrested for having a relationship with 19-year-old Arnold Murray at a time when homosexuality was illegal in the UK.
Aged just 41, he was found dead from cyanide poisoning in 1954 with a half-eaten apple by his side. An inquiry concluded that it was suicide.
Turing was recognised by many for his role in helping crack the Enigma code and bringing an end to World War Two. It is predicted that his work saved the lives of an estimated 14 to 21 million, shortening the war by two to four years.
The files, which will go on display at Chester Town Hall, have been warmly welcomed by the architect of Alan Turing’s pardon, Cllr. John Leech, who said: “I really hope this will go some way to highlighting just how absurd the conviction was, and how rightly deserved the pardon is.
“This is an important public service that I think will help generations to come understand the significance of Turing’s life.
“It’s a great contribution to LGBTQ+ history”.
The former Manchester MP submitted several motions to parliament and campaigned hard to secure the historic pardon. Mr Leech celebrated Turing’s pardon but noted that it was “utterly disgusting and ultimately just embarrassing” that the conviction was upheld as long as it was.
Mr Leech added: “I believe Alan Turing would be so proud to see how far society has moved on and how widely his work is now celebrated.”
At the UK premiere of the film based on Turing’s life, The Imitation Game, the producers publicly thanked Mr Leech for his campaign which brought the injustice to public attention, and for successfully securing Turing’s pardon.
Mr Leech said Turing’s persecution “by the state for being gay was a scandal that shouldn’t have been allowed to stand”.
Following the success of the campaign to pardon Alan Turing, Mr Leech turned to securing the pardon for the 75,000+ other men criminally convicted of sexuality.
Last week the Government said proposals to pardon all gay men convicted under historical gross indecency laws would be brought forward “in due course”.
The files will be on display until 9 October at Chester Town Hall.