The Canadian singer, songwriter and poet died on Thursday at the age of 82.
As a student at Queen's University, Geoff Hill hitchhiked to Manchester to see the Canadian artist in concert.
"I had just finished university and was broke as usual, so I hitched over in freezing weather to see him live.
"It was the first time I had seen him in concert and it was absolutely brilliant - he did seven encores.
"The next day, I was hitching up the M6, and I walked into a motorway cafe and Leonard Cohen was just sitting there, on his own, eating Maltesers out of a box."
Speaking on the BBC's Talkback programme, Mr Hill explained that, although he was keen to speak to Cohen, he was nervous about how the legendary singer would react.
"I was hesitating, but then I just decided that if I didn't go over and say something, I'd regret it for the rest of my life.
"So I went over and said: 'I'm sorry to bother you, but are you Leonard Cohen?' and he said: 'Yes, I am.'
"Then I said I didn't want to interrupt him, but just wanted to say I thought his concert the night before was brilliant."
Mr Hill was taken aback when Cohen expressed thanks and invited him to sit down.
"He said: 'Sit down, have lunch with me' and explained that Maltesers were his favourite sweets when he was in England.
"So we sat there, sharing the sweets and talking about life, the universe and everything."
The Northern Ireland travel writer told Cohen that he had just begun writing a novel, but wasn't sure if he would finish it.
"'You'll finish it', he said, and 10 books later, it looks like he was right.
"He was just the most decent, charming, modest man you can imagine."
The singer then offered him a lift in his tour bus.
"Then he signed my diary and asked where I was going next. I told him I was hitching back to Belfast, and he said: 'Jump in with us - we're heading to Glasgow next.'
"So he brought me up the road, shook my hand and gave me a wave as they drove on - I'll never forget it.
"I was in a daze for, well possibly the rest of my life. It was such a wonderful experience."
A Belfast journalist has recalled fond memories of a brief but moving encounter with Leonard Cohen, who offered him a lift as a hitchhiking student in 1979.