Lawris Sanchez paid the price for a disappointing first half to the season as he was sacked before Christmas.
Ray Lewington has been in caretaker charge for the last two matches but The Cottagers have continued to struggle.
Fulham were keen to make a swift appointment and John Collins had been tipped to take the reins.
However, the club have now announced that Hodgson will become manager on a long-term contract effective from 30th December.
That means Lewington and his assistant Billy McKinlay will once again oversee Saturday's game against Birmingham, before Hodgson takes his place in the dugout for the clash with Chelsea on New Year's Day.
Hodgson has been charged with the task of steering Fulham out of the relegation zone and he is relishing the challenge ahead.
Delighted
"I am delighted to have been offered this opportunity with Fulham," Hodgson, who stood down as Finland coach at the end of November, told the club's official website.
"After long talks with the chairman (Mohamed Al Fayed) and the board I am convinced that we can take the club to a new level.
"I am determined that we will overcome the current position, which I understand will be a challenge, but one that I will relish.
"I am very much looking forward to training with the team on Sunday, and will of course be at St Andrews tomorrow to watch the vital clash against Birmingham City."
