He will take over on 30 December, with caretaker boss Ray Lewington remaining in charge for Saturday's away game against Birmingham City.
Fulham sacked Lawrie Sanchez last week with the club in the Premier League's bottom three.
"I am determined that we will overcome the current position," Hodgson, 60, told the club's official website.
"I understand that it will be a challenge, but one that I will relish."
Fulham's new manager will be at their game at St. Andrews on Saturday before taking training with the Craven Cottage squad on Sunday.
His first game in charge will be a local derby against chelsea on new years day.