Dr Alan Turing died of cyanide poisoning and an inquest recorded a verdict of suicide, although his mother and others maintained his death was accidental.
There has been a long campaign to clear the mathematician's name, including a well-supported e- petition and private member's bill, along with support from leading scientists such as Sir Stephen Hawking.
The pardon under the Royal Prerogative of Mercy will come into effect today.
The Justice Secretary has the power to ask the Queen to grant a pardon under the Royal Prerogative of Mercy, for civilians convicted in England and Wales.
A pardon is only normally granted when the person is innocent of the offence and where a request has been made by someone with a vested interest such as a family member.
But on this occasion a pardon has been issued without either requirement being met.
WWII codebreaker whose work may have shortened the war by two years was persecuted for being gay but pardoned after a long campaign.
During WW2, Alan Turing worked at the Government Code and Cypher School where he devised techniques which cracked the German Enigma code.