Sean Hodgson was sentenced to life in 1982 for the 1979 murder of 22-year-old gas board clerk and part-time barmaid Teresa De Simone, who was found strangled in Southampton.
His conviction was quashed after new DNA evidence revealed he could not have been the killer.
Mr Hodgson, now 57, is one of the longest-serving victims of a miscarriage of justice.
He was present in the dock today to hear the Lord Chief Justice, Lord Judge, and two other senior judges in London order his discharge.
Emerging from the Royal Courts of Justice in London a free man, he waved from the steps at the large crowd of waiting journalists.
Asked how he felt, he said simply: "Ecstatic."
His brother Peter added: "On behalf of my brother, I would like to thank the solicitor a million million times.
"What I would like to say - I've had a dream for 27 years. I know it's a hell of a long time. But it's finally come true."
After recounting the facts in detail of what he described as a "dismal story", Lord Judge said: "This decision leaves some important unanswered questions.
"Perhaps the most important is that we do not know who raped and killed the dead girl.
"We can but hope that, for the sake of the appellant and the family of the murdered girl, that her killer may yet be identified and brought to justice."
At the time of Mr Hodgson's trial, DNA tests were not available, with the world's first use of such evidence in court not taking place until 1986 in Leicester.
But last November, following requests from his legal representatives, Hampshire Police and the Forensic Science Service undertook a comprehensive forensic case review and examination of material, including DNA testing on samples collected at the time of the murder.
In the light of new evidence, the Criminal Cases Review Commission (CCRC) decided to refer Mr Hodgson's case to the Court of Appeal because it considered that there was a "real possibility that the court would consider the conviction unsafe and quash it".
The court heard today that DNA evidence found at the scene did not match a sample given by Mr Hodgson - and there was no forensic link between him and the murder scene.
Mr Hodgson, who is also known as Robert Graham Hodgson and is originally from County Durham, made various confessions to police before pleading not guilty at his trial at Winchester Crown Court.
Miss De Simone's partially clothed body was found in the back seat of her Ford Escort in the car park beneath the Tom Tackle pub where she worked part-time.
Prosecutors at trial relied on the confessions and match of blood type with samples found at the scene.
Mr Hodgson's defence team argued that he was a pathological liar and that the confessions were false.
The Crown did not oppose the conviction appeal today.
Lord Judge said: "The conviction will be quashed for the simple reason that advances in the science of DNA, long after the end of the trial, have proved a fact which, if it had been known at the time would, notwithstanding the remaining evidence in the case, have resulted in quite a different investigation and a completely different trial."
He said that swabs taken from the dead girl had been examined and there were sufficient remnants of sperm on them for proper DNA analysis, resulting in the conclusion that the sample on the swabs did not come from the appellant.
"Whoever raped her - on these findings, it can't be the appellant.
"The Crown's case was that whoever raped her also killed her, so the new DNA evidence has demolished the case for the prosecution."
A statement issued by Mr Hodgson's solicitor, Julian Young, said his client was obviously relieved that his denials had been accepted and his innocence, which he had maintained for so many years, confirmed.
"Sadly, the mother of the victim now has to face the possibility and distress of the circumstances of the case being reopened."
He added: "At a time when the criminal justice system is under scrutiny, it is gratifying to see all parties co-operating to rectify a serious miscarriage of justice."
Mr Young also commented on an aspect of the ruling when Lord Judge pointed out that there was an additional feature of the case "which we must draw attention to".
The judge said the court had been told during the hearing that in 1998 an inquiry was made by solicitors then acting on behalf of the appellant to the Forensic Science Service about the existence of relevant exhibits associated with the murder.
He said "presumably that request would have been made in order to see whether further testing might then be possible".
The judge said the response was that none of the exhibits had been retained and that was "plainly wrong".
He added: "We have been told that the matter has been referred to the appropriate forensic regulator. We can say no more about it until these investigations have been completed."
After the ruling, Mr Young said: "Ten years ago someone in the Forensic Science Service, perhaps by accident, made an error of some sort, and as a result he stayed in custody 10 years longer."
Indicating that further action for compensation was under consideration, he said: "Whether Forensic Science have liability in respect of an error 10 years ago is a matter for another day, when we have a chance to talk to Sean at some length."
Mr Young said no-one was being blamed at the stage when the jury found him guilty on the basis of the evidence before them.
If the jury had known what was known now they "would have almost certainly not convicted him - if he had ever been charged".
Mr Hodgson, who, the court heard, has suffered mental and physical health problems for many years, was now being helped by a miscarriage of justice team and would be visiting healthcare professionals.
It would then be for him "to make his own decision on where he wants to live".
Mr Young said Mr Hodgson was "looking forward one day to going to watch a football match", adding that he believed he was a Sunderland supporter.
Asked about Mr Hodgson's description of himself as "ecstatic", Mr Young said: "That describes him most definitely.
"He is very pleased that the nightmare is at long last over."
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