The Cottagers confirmed the appointment of the ex-Wales, Blackburn and Manchester City boss on a two-year deal.
Hodgson, who led Fulham to the Europa League final last season, created the vacancy when he left the London club for Liverpool last month.
Speaking after the Reds' Europa League qualifier against FK Rabotnicki in Macedonia, Hodgson said: "It is a good appointment. I am very pleased for him and Fulham Football Club.
"I think Mark is a very good manager and he has proved his worth many times. It is good Fulham have got such an experienced man to take over.
"I think he will enjoy working at Fulham because it is a fantastic club with fantastic people and magnificent players. I wish him well but not too well when he plays against us - but I know he will do well."
Source: PA
Source: PA