The defender, who can play at either centre-half or left-back, moved to Turf Moor permanently from Manchester City in 2012 after a productive loan spell.
Mee played a key role in Burnley's promotion from the Championship in 2013-14, making 38 league appearances as Sean Dyche's men ended the campaign with the best defensive record in the division.
"I'm absolutely delighted to sign for another three years," he told Burnley's official website. "I've enjoyed my time so far and hopefully we can have many more seasons like the last one and achieve more things.
"It was an easy decision to make, I've enjoyed my time here, particularly under Sean and it's been a great time since I joined.
"I've settled here really well and I feel right at home here with the fans and all the lads. I'm always improving now and I'm coming into a good age in terms of playing a lot of games.
"I just want to kick on and show everyone what I can do. Last season was a fantastic season for all the lads and we need to go on, push on and top that now which would be really nice."
Burnley's top-flight campaign begins with the visit of Chelsea on August 18.