The 27-year-old has agreed a three year deal at Craven Cottage, with the option of a further 12 months.
Former Tottenham trainee Button moves across west London after playing 141 times during three years with the Bees.
"I understand if there are some fans who will be disappointed we have sold a player to our local rivals," Bees co-director of football Phil Giles said.
"However, I'm confident that we've made a decision that is in the best long term interests of the club."
Button becomes Fulham's seventh signing of the summer transfer window.
Find all the latest football transfers on our dedicated page.
Fulham have signed goalkeeper David Button from Championship rivals Brentford for an undisclosed fee.