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Buckingham became part of horse racing folklore when steering the 100-1 shot through a mass of fallers at the 23rd fence to win at Aintree 49 years ago.
Of 44 starters, only 18 finished.
"It was havoc. Three jockeys turned Foinavon down but I'd have ridden Dick's donkey to be in the Grand National," said Buckingham in a BBC interview in 2010.
"What people don't realise is that we'd got it all planned before we left the weighing room!"
BBC horse racing correspondent Cornelius Lysaght:
Buckingham might not have been the best-known jump jockey of modern times but, unlike many of his higher-profile contemporaries, he has an indelible place in racing history.
Foinavon really was a complete no-hoper in the 1967 Grand National, and was so far behind when the melee took place that Buckingham was able to steer past the incident, and go so far clear that they weren't caught up.
It was quite likely the most dramatic staging in the race's history - at, ironically, the smallest fence on the track, later renamed Foinavon - and even to this day, a regular racecourse refrain is that such and such is "the biggest shock since Foinavon".
Former jockey John Buckingham, who famously won the 1967 Grand National on board Foinavon, has died aged 76.