Former Manchester City boss Hughes emerged as the frontrunner after talks with the Dutchman ran their course, and he will begin work at the club immediately, taking charge of his first match in the friendly meeting with Werder Bremen on August 7.
Hughes acknowledged the success Hodgson enjoyed at the club - most notably taking them to the Europa League final last season - but has already set out his own blueprint for taking them forward.
Hughes told www.fulhamfc.com: "I have discussed my aspirations with both the chairman and (chief executive) Alistair Mackintosh and believe that we are aligned in our aims for what can realistically be achieved here.
"I am joining on the back of two of the most successful seasons in the club's history and that in itself brings with it the challenges of expectation and ambition.
"I am confident that with some additions to the squad, hard work and commitment, we can move this club forward in the right direction.
"I hope the Fulham fans will enjoy some special times during this season's campaign and we will work hard to achieve that.
"I'm looking forward to working with the squad as soon as possible, and in making sure the on-pitch preparations are complete before the first competitive ball is kicked in August."