Mee was available for free after his contract at Burnley expired at the end of June, bringing an end to a 10-year spell at Turf Moor.
The 32-year-old has 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 delighted to add him given the leadership he offers too.
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 squad.
“He had six good years for Burnley in the Premier League. I really love 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 on set-pieces in both boxes. I am looking forward to adding him to the squad.”