He spent 2016-17 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 told his new club's official website.
"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.