Justice Minister Sam Gyimah called it a “truly momentous day”.
Thousands of gay and bisexual men will be cleared of former sexual offences under which they would not be charged for today.
The Government has confirmed that the so-called Turing’s Law – named after World War II codebreaker Alan Turing – takes effect today.
As part of the Government’s Policing and Crime Act, all gay dead men convicted under laws which have now been repealed, will be granted an automatic pardon.
But those who are still alive have to apply to the Home Office to have their convictions removed.
The pardons were first announced last year, and have now been officially rubber-stamped after the Policing and Crime Bill received Royal Assent.
Justice minister Sam Gyimah said: “We can never undo the hurt caused, but we have apologised and taken action to right these wrongs.”
A spokesperson for gay rights charity Stonewall said: “Another important milestone of equality has been secured in law.
“The more equality is enshrined into our law books, the stronger our equality becomes, and the stronger we as a community become.”
Mr Turing, the Enigma code breaker responsible for decrypting Nazi messages, was granted a posthumous royal pardon in 2013.
The pioneering mathematician, whose code-breaking skills are said to have shortened World War Two by two to four years, lost his job with the secret service following a conviction for gross indecency and was forced to undergo chemical castration by a series of injections.
Two years later Mr Turing took his own life.
It is estimated that up to 49,000 were convicted under similar laws until homosexuality was decriminalised.