Olsson was sorry to see Hodgson leave the Hawthorns.
"He's a top man," Olsson told the Birmingham Mail. "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."