The West Bromwich Albion defender is set to come up against his former manager in Euro 2012 Group D, and hailed the impact the ex-Baggies coach has had on his career
Hodgson joined the England set-up from West Brom at the end of the Premier League season, having helped them to a 10th-placed finish.
And the 29-year-old, who won the Baggies' Player of the Year award last term, has revealed he owes a lot to his former boss.
"He's a top man," Olsson told the Birmingham Post.
"I really enjoyed working with him on a professional level, and also a personal level, so I wish him all the best.
"What did he bring to Albion? Two things. One is, how well he organises teams, we've been a lot more solid under him.
"Second, he's brilliant when it comes to inspiring players. You can really see his desire to do well and that impacts on the players.
"It's unusual for an English manager to be that involved in everything at the club, and I really like that."
Sweden face England on June 15 at the Olympic Stadium in Kiev.