The Sweden international left-back, who played in the top flight with Rovers before their relegation to the Championship in 2012, has joined the Canaries on a four-year contract for an undisclosed fee.
Olsson told Norwich's official website: "I'm very happy, it feels good to play in the Premier League again, to be with a Premier League club, so yes I'm excited.
"My dream has always been to be in the Premier League but Rovers went down into the Championship, which was a good lesson for me. I learned a lot of things.
"But I'm at a new club right now, so I'm looking forward to meeting the players and enjoying my time here."
The 25-year-old is also relishing the prospect of working with Norwich boss Chris Hughton after arriving at Carrow Road.
"I had a few clubs (interested) but I think Chris gave me a good idea of how they wanted to play and the ambition of this club," he added.