"I'm delighted to have been offered this opportunity with Fulham," Hodgson told the club's official website.
"After long talks with the chairman and the board I'm convinced that we can take the club to a new level.
"I'm determined that we'll overcome the current position, which I understand will be a challenge, but one that I will relish.
"I'm very much looking forward to training with the team on Sunday, and will of course be at St Andrew's tomorrow to watch the vital clash against Birmingham City."