Chambers only recently penned a new four-year deal with the club, but boss Unai Emery is happy for him to go out and play regular first-team football with the newly promoted Cottagers.
The 23-year-old jumped at the chance to move across London and is looking forward to the season ahead.
Chambers told fulhamfc.com: "I watched a lot of Fulham last season, I really like the way they play football, there's a good manager, 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."
Fulham director of football operations Tony Khan added: "Calum is a versatile defender with Premier League experience, and the combination of his strong data profile and the positive reports from our scouting department confirm that he's a tremendous talent."
It now remains to be seen if the Gunners will look to sign a replacement before the transfer deadline, with Bayern Munich's Boateng a reported target.