The 23-year-old, who can operate on the wing or a central striking role, has penned a two-and-a-half-year contract with Rovers.
He becomes Blackburn's second signing of the January transfer window, with Anthony Modeste having been drafted in on loan.
Olsson will find one familiar face waiting to greet him at Ewood Park, with his twin brother Martin already on Blackburn's books.
Both brothers took in a trial with Rovers back in 2005, but Martin was the only one to be offered a permanent stay.
Marcus Olsson has had to be patient in his pursuit of a Premier League opportunity, but he has now been offered the chance to further his career in England.
His development in recent years was rewarded with his first senior outings for Sweden in early January and he will be hoping to earn further recognition during his time with Blackburn.
The club are waiting on international clearance from the Swedish Football Association and FIFA before adding Olsson to their ranks.
