The 23-year-old Southampton academy product moved to Emirates Stadium in 2014 and won three senior England caps during that season.
He spent 2016-2017 on loan at Middlesbrough before returning to Arsenal last time around to make 12 Premier League appearances over the course of Arsene Wenger's final campaign in charge.
"I'm really excited. I watched a lot of Fulham last season, I really like the way they play football," Chambers said.
"There's a good manager and it's a great club, so I'm really excited for the season ahead.
“Everyone can see that Fulham's a club that likes to play football, play football from the back, through the lines. That's the style of football I like as well, so I think it fits me and suits the way I play."
Slavisa Jokanovic's side begin their top-flight return at home to Crystal Palace on Saturday and have made a number of eye-catching signings, including Jean Michael Seri, Aleksandar Mitrovic and Andre Schurrle.
Chambers is the latest defensive reinforcement after Alfie Mawson joined from Swansea City last week but Celtic rejected an approach from Craven Cottage for their Belgium centre-back Dedryck Boyata.