The Northern Ireland Court of Appeal ruled the conviction was unsafe and unsatisfactory because there was a reasonable possibility that Mr Hill's confession to the murder had been induced by inhuman treatment by Surrey police officers.
The three judges, headed by the Northern Ireland Lord Chief Justice, Sir Brian Hutton, said that for police to point a revolver at Mr Hill, as could have happened, was 'a disgraceful and grossly improper action which clearly constituted inhuman treatment'.
But the judges also indicated several times in their judgement that they believed many of Mr Hill's allegations of ill- treatment by police were untrue. They also dwelt on the point that some confessions extracted by improper means were in fact accurate.
No mention was made of the 15 years Mr Hill spent in prison for the Shaw murder and the Guildford and Woolwich bombings. After reading the judgment Sir Brian glanced at Mr Hill, nodded, and said simply: 'The appellant is free to go.'
Mr Hill, 39, was accompanied in court by his wife Courtney, daughter of the late Robert Kennedy, by his mother-in-law Ethel Kennedy, and other relatives. Outside the court he told reporters: 'I want to lead a normal life now. I've been in limbo for a long time. I didn't wait for 17 years to be told I was innocent of this - I always knew I was innocent of this.
'I am very relieved that this part of my life is over. If we're on the road to peace, if there is to be a peace process, then justice has to be the first step along that road.'
Mr Hill, who now lives in America, was released from prison in October 1989 with the other members of the Guildford Four after Crown counsel said evidence had come to light which threw doubt on the honesty and integrity of a number of the Surrey officers investigating the case. But the Shaw conviction stood until yesterday.
The quashing of that conviction means Mr Hill will now be entitled to compensation of up to half a million pounds for the years he spent in jail. An independent assessor is to make a recommendation on damages to the Home Secretary, Michael Howard.
The hearing was attended by several relatives of Brian Shaw, the victim, who left the Army in 1974 to marry a Belfast woman. He was abducted from a bar and shot dead by the IRA within weeks of moving to Belfast. His widow, Maureen Hall, who has re-married and has two teenage children, said after yesterday's verdict: 'We felt that the Kennedy circus was designed to put extra pressure on the judges to find in Paul Hill's favour. Naturally we are disappointed with the verdict.
'We have to live with this decision, but we do not have to agree with it. Brian Shaw was the real innocent victim in this case.'
A report is due this summer from Sir John May, a former judge who was appointed by the Government to investigate the handling of the Guildford Four and Maguire Seven cases. He is to study the Paul Hill appeal judgment before submitting his final report within the next few weeks.
Leading article, page 17