Sir Chris, who is Britain's most successful Olympian with six gold medals in cycling, carried the symbol down The Mall.
The Queen, who is head of the Commonwealth, then launched it on its 248-day journey to the 70 countries and territories by handing it to another Scots Olympic gold medallist, sprinter Allan Wells.
Sir Chris, from Edinburgh, was joined by the Pipes And Drums 1st Battalion Scots Guards and the Pipes And Drums 1st Battalion The Royal Regiment Of Scotland (Royal Scots Borderers).
Bagpipes greeted the waiting guests and dignitaries who had gathered on the forecourt for the relay's official launch, but it was the sound of a helicopter that annoyed Scottish violinist Nicola Benedetti as she played at the handover to Wells.
She performed the Robert Burns song My Love Is Like A Red, Red Rose for VIPs while a helicopter whirled noisily overhead, As the star left stage, she pointed at the helicopter and said: "I had a lot of competition from that."
Sir Chris later put a picture on Twitter, the networking site, of himself walking up The Mall with the baton. He wrote: "Very proud 2carry the baton 2the steps of Buckingham Palace 2day 2start its journey around the Commonwealth."
While staying at Balmoral over the summer the Queen had written her message to the athletes to mark the start of the relay.
But her words will remain a secret until she reads it aloud at the opening ceremony of the Games at Celtic Park next July 23.
The relay is a Commonwealth tradition that started in 1958, growing in size and scale with every Games.
It shares similarities with the Olympic torch relay and is designed to unite the citizens of the Commonwealth in a celebration of sport, diversity and peace.
Glasgow 2014 will be the 20th Commonwealth Games and the baton relay route is the biggest so far.
It is travelling to Scotland today before heading to India for its first international stopover tomorrow.
Other participants at yesterday's ceremony were Izzy Conway, a volunteer or Clydesider at the games; Aamir Meymood, the 13-year-old Shawlands Academy pupil who designed the Glasgow 2014 tartan; games ambassador Julie McIlroy; and 12-year-old Beth Gilmour, who was accompanied by games mascot Clyde, whom she designed.
The baton will travel through Asia, Oceania, Africa, North and South America, the Caribbean and Europe.
Some doubt was cast over the Indian leg of the tour after reports from the country suggested it was unable to host it due to the Hindu festival of Dussehra, but organisers of the relay said it would go ahead.
The baton was originally due to travel to 71 nations and territories in total, but Gambia pulled out of the games after officials said it did not consider itself to be a "neo-colonial institution".
First Minister Alex Salmond, who was also at the relay launch, said: "2014 promises the greatest-ever Games and the relay will provide a fantastic celebration of sport and culture across the Commonwealth, with Glasgow and Scotland at its heart."
l Prince Tunku Imran, president of the Commonwealth Games Federation, and Kamalesh Sharma, secretary general of the Commonwealth of Nations, are to be given honorary degrees by Glasgow next June, just over a month before the Games begin.