Mee was available for free after his Burnley contract expired at the end of June, ending a 10-year spell at Turf Moor.
The 32-year-old signed a two-year contract with Brentford after undergoing his medical in west London on Thursday.
The defender brings a wealth of experience and the bees are happy to add him given the leadership he also offers.
Brentford head coach Thomas Frank said: “I am very happy that we have signed Ben. He will add a lot of quality and experience to the team.
“He’s had six good years for Burnley in the Premier League. I really like his defensive mindset; he knows how to defend the box, he knows how to block a shot and he knows how to win duels.
“He will bring leadership and communication to the team, which is very attractive. He has a very good left foot and will be very good for us from set pieces in both squares. I can’t wait to add him to the team.