The versatile 25-year-old became the Canaries' fourth signing of the summer as they wrapped up a deal with Blackburn Rovers on Wednesday.
A move to Carrow Road has allowed Olsson to step back up into the Premier League.
His representative claims that was always the intention, with it reported that Russian outfit Kuban Krasnodar had also seen an offer accepted by Blackburn.
Hasan Cetinkaya told Expressen: "It's a step in the right direction for Martin, both football-wise and financially. He joins a club which is investing and with a good atmosphere.
"There was big interest, both in England and other leagues.
"But Blackburn didn't want to sell in the past."