Alistair Panton told BBC Radio Five Live: "I missed seeing Andy win in London and I think that's why I came out here to see him win in Rio."
He flew back to Aberdeen just hours after Murray's victory over Juan Martin del Potro.
Murray became the first tennis player to win two Olympic singles titles.
The 29-year-old secured a 7-5 4-6 6-2 7-5 victory to make it GB's most successful day at an overseas Games with five gold medals.
The see-saw match at the Rio 2016 Olympics featured 14 breaks of serve.
The day before the final, Mr Panton said he had gone to watch Aberdeen play Hearts while keeping an eye on the result of Murray's semi-final with Japanese fourth seed Kei Nishikori.
"Of course Andy progressed, by which time I was making my way to the airport from Aberdeen, down to London and constantly trying to book my trip as I went along - from London to Sao Paulo and then down to Rio," he said.
Mr Panton, who lives in Aberdeen, said he had made a similar trip to Melbourne for the Australian Open in January, when Murray was defeated in three sets by Novak Djokovic.
But he said he was not the only fan to go to such lengths to follow one of his favourite sports stars around the globe.
"There are a couple of others. There's a guy from New Zealand who travels over as well," he told the BBC.
"I love being there for the big moments. I've missed a couple in the past and you think, I wish I was there as life's so short - just go for it."
Speaking at the match, Mr Panton said he had no plans to stay on in Rio to watch other events.
"The last flight out of here is back to Portugal tonight so I've got to be on that," he said.
An Andy Murray super-fan has said he impulsively booked tickets to Rio to watch the Olympic final after seeing the tennis ace get through the semis.