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.
David Cameron has paid tribute to Alan Turing for his role in "saving Britain in World War Two" after the famous code-breaker was awarded a a posthumous royal pardon.
The Prime Minister said: "Alan Turing was a remarkable man who played a key role in saving this country in World War Two by cracking the German Enigma code.
"His action saved countless lives. He also left a remarkable national legacy through his substantial scientific achievements, often being referred to as the father of modern computing."
Second World Warcode-breaker Alan Turing has been given a posthumous royal pardon for a 61-year-old conviction for homosexual activity.
Dr Turing, who was pivotal in breaking the Enigma code, arguably shortening the Second World War by at least two years, was chemically castrated following his conviction in 1952.
His conviction for "gross indecency" led to the removal of his security clearance and meant he was no longer able to work for Government Communications Headquarters (GCHQ) where he had continued to work following service at Bletchley Park during the war.
Dr Turing, who died aged 41 in 1954 and is often described as the father of modern computing, has been granted a pardon under the Royal Prerogative of Mercy by the Queen following a request from Justice Secretary Chris Grayling.
"Dr Alan Turing was an exceptional man with a brilliant mind," Mr Grayling said.
One of Oskar Schindler's lists has been posted on the eBay auction website with a starting bid request of $3 million (£1.97 million).Read the full story ›
The only surviving German Second World War Dornier Do 17 bomber has been lifted from its watery grave in the English Channel. The aircraft was shot down off the Kent coast more than 70 years ago during the Battle of Britain.
The project is believed to be the biggest recovery of its kind in British waters. Attempts by the RAF Museum to raise the relic over the last few weeks have been hit by strong winds but today, the operation was finally successful.
Thousands of Irish soldiers who joined the British Army to fight Nazi Germany will be officially pardoned today.
The Irish Government will pass special legislation which grants an amnesty to the former troops who were branded deserters for joining up.
Rules bought in during the Second World War saw these ex-soldiers face widespread discrimination such as being barred from state jobs and refused military pensions.
Dublin's Justice Minister, Alan Shatter said "unfortunately, many of the individuals whose situation is addressed in this Bill did not live to see the day that this state finally acknowledged the important role that they played in seeking to ensure a free and safe Europe."
A rare German Enigma machine used during World War Two will go under the hammer today.Read the full story ›