The 28-year-old has moved to the Liberty Stadium for a reported £4 million fee.
The deal includes the option of a third year for the Sweden international, should both sides want to commit to an extension further down the line.
A switch to South Wales offers Olsson a welcome return to a Premier League stage, having suffered relegation out of the top-flight with Norwich last season.
Olsson has spent much of his career to date at the highest level in English football, having made the breakthrough at Blackburn Rovers in 2007.
He moved on to Norwich after six seasons at Ewood Park, taking in two relegations and a promotion during his time at Carrow Road.
Olsson is Paul Clement’s second signing of the January transfer window, with one deal already wrapped up for PSV winger Luciano Narsingh.
He will add to Swansea’s options at left-back, with cover needed as Neil Taylor works his way back from a fractured cheekbone.
Olsson will be hoping to avoid suffering a fourth slip out of the Premier League with the Swans – having also been relegated with Blackburn – but knows there is work to be done with the club propping up the division, albeit one point from safety