The 25-year-old, who can also operate on the left side of midfield, will move to Carrow Road on a four-year deal from the Championship club once all of the relevant paperwork has been completed.
Olsson has been a long-term target of Canaries manager Chris Hughton, who has been on a summer spending spree following the club's record £8.5million capture of Holland international Ricky van Wolfswinkel, while England Under-21 winger Nathan Redmond was last week purchased from Birmingham, and defender Javier Garrido has signed permanently after a loan from Lazio.
"We are delighted with the addition of Martin. He's been playing in England for seven years and is well acclimatised to the Premier League," said Hughton on the club's official website.
"He can also play anywhere on the left hand side so he brings us good flexibility in that sense, plus at 25 he's at an age where he has some experience and also some time to improve.
"At this time it is about improving the squad that we have and Martin certainly does that."
Hughton is expected to show no let-up in his summer recruitment drive, with Scotland defender Russell Martin on Tuesday signing on for another three years with a contract extension.
Norwich are understood to be tracking PSV Eindhoven's Sweden international Ola Toivonen, Lokomotiv Moscow's £6million-rated Senegal striker Dame N'Doye.
Feyenoord midfielder Leroy Fer and Ajax defender Toby Alderweireld, meanwhile, are also reported targets for the Canaries, with suggestions the duo have already travelled to East Anglia to take in the club's facilities ahead of undergoing medicals.
Norwich are currently in Austria for a training camp ahead of a three-match tour to the west coast of the United States later this month.