Derek Burns, from West Calder in West Lothian, died after he was struck by a train in London in March 1989.
His father, who was praised for working tirelessly in the intervening decades to trace his son, expressed relief at the identification, saying it would help put the family's minds at peace.
The train death was not seen as suspicious at the time, with a coroner recording an open verdict, although police were unable to identify the body.
The man was buried in the Islington and Camden cemetery in London.
Recent inquiries by the British Transport Police established that on the day he died, Mr Burns had visited his girlfriend at her home near West Hampstead station before discovering she was ending their relationship.
Mr Burns had been reported missing to Lothian and Borders Police the day before his death and was never seen again after visiting his girlfriend.
Following the breakthrough, a DNA sample was taken from the body in the cemetery, as well as from Mr Burns's family, with tests later confirming the dead man's identity.
Derek Burns Snr described his son as a "happy boy", adding: "We did many things together as a family and he and his older brother had great times together."
He recalled the day his son disappeared and said: "The morning he went missing I was going to the Borders and popped into his room to see if he would like to come with me.
"The weather was awful and he said 'no thanks dad', so I said okay and left.
"He did not appear for dinner that night or contact us, which was very unusual for him as he was a home person.
"We subsequently found out that he had gone to London to see his girlfriend and find a job.
"I think it may have been a spur-of-the-moment thing as he left without his driving licence, passport or any spare clothes or toiletries.
"There had been no place to stay at his friend's flat in London, so he left to come home, and the lack of identification has been the major cause of delay in identifying him."
He added: "We are relieved that our son has now been found and we can at last put our minds at peace.
"We are very grateful to the police for the work and effort they've put in, and would also like to thank the charity Missing People for the help and assistance we've had over the years."
Detective Chief Inspector Simon Taylor, of the British Transport Police, said: "The man's death in West Hampstead was fully investigated at the time and all possible lines of inquiry were followed up to try to establish his identity, but without success.
"However, the piecing together of clues and other circumstantial evidence led us to the theory that the man was Derek Burns, with DNA profiling confirming his identity."
He added: "Derek Burns's family will clearly have many unanswered questions about what took place that day, and about the circumstances leading up to Derek's death, but we hope this will provide them with some comfort, solace and ultimately a form of closure."
Mr Burns's body will be repatriated to Scotland, where a funeral will be held in due course.
Martin Houghton-Brown, chief executive of Missing People, said: "The thoughts of the staff and volunteers at the charity Missing People are with the family and friends of Derek Burns at this very sad and difficult time."
He also thanked Mr Burns Snr for his fundraising efforts for the charity, after he walked more than 1000 miles to raise awareness of the charity while searching for his son.
Mr Houghton-Brown said: "He has helped us to be able to continue to search for the 250,000 people who go missing every year and support their families left behind."