The Premier League club have announced the 24-year-old has agreed a four-and-a-half year contract at Turf Moor with the option to extend for a further 12 months.
Brownhill is manager Sean Dyche’s first signing of the January transfer window.
Brownhill said: “It’s a really good feeling to be at Burnley. It’s a big football club with a great fanbase.
“Every time I’ve played here it’s been nice to play at Turf Moor and I’m really excited.
“I’ve always wanted to get to the top. It’s been mine and my family’s goal ever since I played football as a kid.
“I’m thankful to Burnley for giving me that opportunity and I am going to take it.”
Warrington-born Brownhill began his career at Preston before moving to the Championship Robins in 2016.
— Bristol City FC (@BristolCity) January 30, 2020
Moving in the opposite direction is Clarets forward Nahki Wells, also for an undisclosed fee.
City have confirmed Bermuda international Wells, who had been on loan at QPR since summer 2018, has signed a three-and-a-half year deal at Ashton Gate.
Manager Lee Johnson said: “Nahki is a player with so much talent and he is a proven goalscorer at this level.
“I have spoken before of our ability to create a lot of chances and I think Nahki will help us in terms of that clinical edge which we have needed at times.”
Wells has scored 15 goals for QPR this season, 13 in the Sky Bet Championship.