The 23-year-old has moved for an undisclosed fee and will join his new team-mates when pre-season training begins on Wednesday.
"I'm feeling good, I'm looking forward to it, it's a big club," Clarkson told City's official website. "I've spoke to a few people about it and they're passionate about their football. As a player you want to be at a club that's passionate about their football."
Clarkson is hoping that the move can boost his international career. He has made two appearances for Scotland, scoring once, and is looking forward to winning more caps now he has moved to England.
He added: "Moving here will help my chances of getting into the squad more often. I'm still young, I've got a lot to learn and Bristol City will be a great club to do that."
Robins manager Gary Johnson was also thrilled to conclude the deal and said: "We've been keeping an eye on him and he's got himself into the Scottish international set-up, he's only 23 and one for the future as well and probably has still got more potential. I'm very pleased with the signing. I think in a couple of years time he'll be worth a lot of money. He's got a lot of ability."