Scotland international Iwelumo, 31, follows former Hull midfielder Dean Marney to Turf Moor after sealing a two-year deal.
Clarets boss Brian Laws said: "I'm delighted to bring Chris Iwelumo to Burnley, I think he is going to be a fantastic addition.
"Chris is not a gamble, he is proven in the Championship and has been promoted four times. He has also averaged about 15 goals a season which tells you he can play.
"His link-up play and knowledge of the game are great and he will be fantastic for the dressing room. He's a winner and can give us something different."