Gold was taken by Hungary’s Daniel Gyurta.
“I loved it and I had a bit more to give today,” said a beaming and surprisingly unruffled Jamieson after finishing the race in 2min 7.43secs.
Jamieson thanked his fans who have been tweeting him their support all day, saying: “I’ve had so many messages today. It’s unbelievable.”
“It’s so much easier to swim with confidence behind you like I did,” Jamieson told the BBC.
“I was desperate to get on the podium. I know how strong Gyurta is, his last 50m is the strongest in the world no doubt, the idea was to make a move before then, and try to cling on. I’m so delighted.”
Scottish Jamieson set a new British record of two minutes 8.20 seconds when he qualified for the final alongside teammate Andrew Willis on Tuesday, giving him a confident start to the race.
The 23-year-old originally planned a career in football before opting to concentrate on swimming.
“It is a great achievement for Michael to reach tonight’s final,” manager Neil Lennon told Celtic’s official website.
Jamieson’s team-mate Andrew Willis finished number eight in 2:09.44