The newly-promoted Premier League club are reported to have spent in the region of £7m to bring the 28-year-old midfielder to Turf Moor.
Defour, who has won 46 international caps for Belgium, has agreed a three-year deal with the Clarets, which will be activated once he receives international clearance.
The midfielder has previously played for Genk, Standard Liege, Porto and Anderlecht, and in that time won four league titles - two in Belgium and two in Portugal.
"I hope I can bring my experience to the team and the club to stay in the Premier League," Defour told Burnley's official website. "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.
"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.
"I also called a friend of mine who plays at Brentford and he told me Burnley was the best team in the Championship and that it would be a really good choice for me."
Manager Sean Dyche added: "Steven was a target of ours and it's been a hard deal to do, but we got there in the end. He's a good player with a depth of experience at international level and also Champions League. Steven is new to the Premier League but has a real thirst and desire to be successful in this campaign."
Defour will wear the number 16 shirt.