Eagles held talks with Rangers earlier in the summer and has also been linked with Celtic, Bolton and Sunderland but the 24-year-old has committed himseld to Burnley until June 2012.
Jubilant Clarets boss Brian Laws said: "Chris has agreed to sign a new two-year deal and is going to stay with us.
"That's great news for the fans and the football club because quite clearly he has the talent.
"He is taking on board what we are asking of him. It's really pleasing that he has committed himself to the club. It quashes any rumours about Celtic or Rangers.
"He wants to stay at Burnley and that's good enough for us."