The medal haul was a record for Team Scotland in the Games, winning 19 gold, 15 silver and 19 bronze, to finish fourth in the overall medal table.
Almost 200 athletes boarded five open-top vehicles outside Kelvingrove Museum in the west end of the city as crowds gathered, cheering and waving flags as they passed on their way to George Square. There, they will be welcomed on to a stage in front of a 5,000-strong crowd.
The athletes held signs saying "thank-you Scotland" and were greeted by a round of applause as they were led out of the grounds of Kelvingrove by a pipe band at about 4.15pm.
Some medal winners, such as Eilidh Child and Lynsey Sharp, are unable to take part in the parade because they are competing at the European Athletics Championships in Zurich, but others such as cyclists Neil Fachie and Craig Maclean, judo sisters Kimberley and Louise Renicks and swimmers Ross Murdoch and Erraid Davies are on board the vehicles.
Popular boxer Charlie Flynn, who won gold in the lightweight division and became an instant hit with his post-bout interview, is also taking part.
Speaking before the parade set off, he said: "It's unbelievable, it's time to reunite with everybody again and see all the faces and get that buzz back.
"All the crowd behind you, it's too good. The support is too good.
"I'm looking forward to hearing the roar of the crowd and the fans, and reuniting with the public and everybody and the noise. It's going to be brilliant, I can't wait."
Scotland fielded its largest-ever team at Glasgow 2014, made up of 310 athletes, with around 190 including cyclists, swimmers, hockey players and the lawn bowls team enjoying today's parade.