The Lancashire outfit have signed the 28-year-old Belgium international in a club-record £7.35million deal from Anderlecht.
He told Burnley's official website: "I hope I can bring my experience to the team and the club to stay in the Premier League. I'm looking forward to every game.
"The atmosphere around the league is fantastic and everyone across the world has seen the Premier League, so I am very proud to be a part of that. It is a new challenge for me, but I like that."
He added: "It has been a long few weeks, but I am very happy to be here.
"When I knew that Burnley was interested, I took some time to look into the club and I saw some interesting stuff.