Edinburgh-born Laidlaw, who lived at Drumoig with his sister Jennifer, was admitted to Ninewells Hospital in Dundee last Saturday, having tested positive for Covid-19.
He started out as a copytaker on the Pink News before becoming the golf reporter for the Edinburgh Evening News.
After a spell in television, first with STV then Grampian TV and, finally, the BBC as its news anchor in Edinburgh, he returned to the golf beat with the London Evening Standard.
He then started to combine television and radio assignments on weekends and for 15 years he was BBC Radio’s golf correspondent.
A move to full-time broadcasting followed with British Satellite Broadcasting, which was taken over by Sky TV, and, latterly, on The Golf Channel.
In 2013, Laidlaw became the first non-American golf writer to cover The Masters for 40 years, joining an exclusive club.
Throughout his career, he covered 165 majors including 58 Opens and 42 Masters.
He was the recipient of the Jack Nicklaus Memorial Award for golfing journalism and earned a lifetime achievement award from the PGA of America, the PGAs of Britain, Scotland and Europe.
Tributes to Laidlaw were led by Sky Sports Golf commentator Ewen Murray.
He wrote on Twitter: “He was my mentor at the start of my TV career. A gifted broadcaster, an exceptional man in every way. Many hearts are sore.”
Dougie Donnelly paid tribute to a “dear friend and colleague”.
He added: “Renton was an outstanding writer and broadcaster, held in genuine affection by everyone he worked with, and a great support to me and to so many others over the years. He will be very sadly missed.”
Iain Carter, the BBC’s golf correspondent, said Laidlaw had been the “voice of golf on BBC radio for so many years and a colossus of the golfing media”.
Paul Lawrie described Laidlaw as a “lovely man” while fellow player Stephen Gallacher said he was “an absolute gentleman and the true voice of golf”.