He was 73 and passed away at a nursing home in Kelso, where he had been since suffering a stroke last year.
Born and bred in the borders, Haldane served his apprenticeship with Stewart Wight and then moved on to Ken Oliver.
In all, he rode around 100 winners in a 12-year career as a jump jockey before retiring from the saddle in 1972, shortly after Slaves Dream finished a two-length second to Quick Reply in the Scottish Grand National.
Oliver's widow, Rhona, said: "We are all very sad to hear of the death of 'Swannie'. He was such a character – nothing 'Swannie' Haldane went on around here that he didn't know about.
"He rode some good winners for us, including Pappageno's Cottage, who broke the course record at Cheltenham one New Year's Day in the Fred Withington Chase and they were also a close third in the 1967 Scottish National.
"On another occasion, we got Pat Taaffe over to ride Happy Arthur at Haydock and they were brought down at the first. 'Swannie' took over the very next day and they went on to win – he dined out on that story for ages.
"We used to say he broke a leg for fun, but he had very brittle bones and drank gallons of milk. Everybody liked 'Swannie' and he will be missed in the racing community."
Haldane's training career, spread over several yards, started in 1981 and the best horses he trained were Border Knight, What A Fiddler, and Highlandman, who was runner-up in the 1997 Fox Hunter Chase at Aintree.
He trained 29 winners over jumps, seven on the Flat, plus several more in point-to-points, and his final winner under Rules was Camp Hill, ridden by Jim Crowley, at Carlisle in March 2004.
His last runner under Rules was at Perth in May 2009 with Billsgrey, who is now trained by Willie Amos.
* Top Scots-owned sprinter Borderlescott has been retired after a glittering career that yielded 14 victories and and almost £776,000 in prize money from his 66 races.
Trainer Robin Bastiman decided his run at Dundalk last month would bring the curtain down on the 10-year-old's racecourse appearances after consulting owners James Edgar and William Donaldson.
The Yorkshire handler said: "He was telling us in his own way after the race in Ireland that he'd had enough and his owners have given him to my daughter Rebecca so he will always remain part of the yard.
"He's taken us to some big days and great occasions. There's always quicker and younger horses coming along – that's the way things go."
Borderlescott won the Nunthorpe Stakes in 2008 and 2009 and other highlights included the 2006 Stewards' Cup, the same year that he was a close second to Fonthill Road in the Ayr Gold Cup.