The 29-year-old ended speculation regarding his future by signing a new four-year contract at The Hawthorns on Friday.
Olsson claimed that he is enjoying life at the club after their fine start to the season and admitted that the influence of his manager proved decisive in contract negotiations.
"It's been a long process but it's done now and I'm very happy," the Sweden international told the club's official website.
"Finally we came to an agreement and I'm very happy. The boss was a key factor for me.
"I really enjoyed playing under Roy Hodgson. The new gaffer has picked up where he left off and, in addition to that, has brought in some very interesting ideas. I really enjoy his way of thinking about football."
The Baggies are currently in sixth place in the Premier League, with 11 points from their first six games.