Andrew Whitby, 51, from Teddington, south-west London, was recognised by the Guinness Book of Records.
He underwent the operation after experiencing health problems associated with a lifelong heart defect.
He appealed for people to sign the organ donor register, describing transplantation as "life-changing".
Figures published by the NHS on Monday show the number of people in the UK donating organs after death has fallen for the first time in more than a decade.
Mr Whitby was born with a hole in the heart, which doctors predicted would mean he was unlikely to live more than a few years.
He defied expectations and lived normally until the age of 20, when his health began to deteriorate.
Mr Whitby developed problems with his lungs and eventually one collapsed, which led to the decision to attempt a heart-lung transplant.
When the procedure was carried out in 1985 at Harefield Hospital in north-west London, he was only the ninth person to undergo it in the UK.
Heart-lung transplants are relatively rare because there are few suitable donor organs available and priority is normally given to people who only need a heart transplant.
Mr Whitby used the occasion of the 30th anniversary of his transplant to draw attention to the need for organ donors.
He said: "My heart-lung transplant has improved and extended my life beyond measure.
"We need more people to sign the organ donor register - without donors, where would that leave people like me?"
Andre Simon, director of transplantation at Harefield Hospital, said: "Andrew's world record shows how a person's life can be completely transformed through the gift of organ donation."
A man has celebrated 30 years since his heart-lung transplant - thought to be the longest anyone has survived after the procedure.