The city is vying with five others to host the 2018 event and swimmer Jamieson, from Robroyston, believes his home city would be the perfect choice.
Glasgow's bid has young people at its heart as it seeks to capitalise on the opportunities created by London 2012 and the Glasgow 2014 Commonwealth Games, as well as its world-class sporting events programme.
The Glasgow 2018 Be A Champion In Your Life campaign has already won the support of Prime Minister David Cameron and Olympians, including Dame Kelly Holmes.
And in a message of support for Glasgow's 2018 bid, Jamieson spoke of his Olympic journey and the support he received while training in the city.
The 23-year-old, who won silver in the 200m breaststroke at the London Olympics and also the Delhi 2010 Commonwealth Games, said: "I'm a champion in my life and I support Glasgow's bid to host the 2018 Youth Olympic Games in Glasgow.
"My journey started at the Glasgow Club, Springburn, when my parents bought me a six-week block at the Learn To Swim programme.
"When I was 12, I moved to Glasgow School Of Sport. That, coupled with a move to the City Of Glasgow Swim Team at Tollcross, was when I made the decision this was the career path I wanted.
"I knew then I wanted to be an Olympian.
"I had five years at the school that gave me a great head start in teaching me life skills I still use today as a professional athlete. I learned about time management, organisation and balancing my academic studies with my sporting commitments.
"When I was a youngster it was all about getting to the Olympic Games and winning an Olympic medal and it was around 2007 when it became a realistic target. I prepared for this year and prepared to win a medal at the Olympic Games. It has been a bit of a whirlwind since the Games but that has been my career highlight so far."
Glasgow believes it will have the infrastructure to run the 12-day event in 2018, which would attract 3600 athletes aged 15-18 participating across all of the 28 summer Olympic sports.
A shortlist of candidate cities will be made next January.
Nanjing, in China, will host the event in 2014.