It follows a sustained campaign by scientists, including Stephen Hawking, and a petition to Government signed by more 37,000.
Announcing the change of heart, the Justice Secretary Chris Grayling said Turing deserved to be "remembered and recognised for his fantastic contribution to the war effort" and not for his later criminal conviction.
"His later life was overshadowed by his conviction for homosexual activity, a sentence we would now consider unjust and discriminatory and which has now been repealed," he said. "A pardon from the Queen is a fitting tribute to an exceptional man."
The pardon under the Royal Prerogative of Mercy will come into effect today.
Since 1945, only three high-profile pardons have been granted in England and Wales under the Royal Prerogative: to Timothy Evans, Derek Bentley and Michael Shields.
- UK Independent