Robert Millar rode it to win the King of the Mountains title in the 1984 Tour De France.
Now, 30 years on, the bike, which was built specifically for Millar, will be displayed at a bike shop in the Saltmarket, alongside the King of the Mountains Polka Dot jersey he won.
Millar gave the jersey to the then owner of Billy Bilsland Cycles, William "Billy" Bilsland, as a gift to his friend and fellow Peugeot and Raleigh cycling professional.
They met at Glasgow Wheelers cycling club early in their careers.
Billy, 68, from Robroyston, also had an eventful career, riding in the 1968 Olympics, the Commonwealth Games in 1966 and winning a stage in the The Tour of Czechoslovakia Peace Race in 1967.
The family has a long cycling history, and Billy's father-in-law was the famous Arthur Campbell, who was an influential administrator in the sport and president of the Scottish Cyclist Union for 32 years until 1984.
The shop, now owned by Billy's son Neil Bilsland, 35, is hoping the one-off historical items will attract cycling fans from far and wide.
Mr Bilsland said: "It's fantastic to have the actual bike that Millar rode to victory here in the shop beside the famous and unique jersey from '84.
"This is a significant piece of cycling history that we are delighted to share, not just in terms of its importance to cycling but also the friendship my father and Robert established in their early cycling careers."
The bike is a Vitus Peugeot model, specifically built for Millar which he previously nearly sold to a private collector.
Millar, who was raised in Glasgow, attended Shawlands Academy and is still the only person from an English native speaking country to have won the Mountains classification of the Tour de France. He rode the Tour 11 times and was the first British rider ever to win a major Tour classification.
The shop is considered one of the leading independent cycling shops in Scotland and supports youth cycling talent in Glasgow with the sponsorship of the Glasgow Cycle Team and Glasgow Riderz.