The 25-year-old hhas signed a three-year deal, arriving from Standard Liege, where he has spent the last four seasons, making 123 appearances, scoring 12 goals in the process.
An Anderlecht academy product, the Meux-born central midfielder has spent time in Italy and played for Belgium at Under 19 and U21 level, before opting to represent DR Congo senior side.
After joining the Clarets, Bastien said: "I'm very proud to join Burnley Football Club.
"I'm excited to discover the Championship, in my new colours.
"I can't wait to get started, begin pre-season and meet my new teammates."
Manager Vincent Kompany said: “Samuel is a great addition to our team.
"He is a high energy midfielder, who can link up play, works very hard and recovers the ball well.
“We are delighted to add Samuel to the group and look forward to welcoming him to our squad.”