Eagles, who rejected a move to Scottish Premier League champions Rangers in the summer, put pen to paper on a deal running until June 2012.
The 24-year-old joined Burnley from Manchester United two years ago and has set his sights on helping the club to return to the Premier League.
"I wouldn't have signed if I didn't think Burnley can get back into the Premier League," Eagles told the club's official website.
"I love it here and the players we have got have got the talent to go back there.
"I have been here for two years and had a brilliant time and with the squad we've got here I believe we can do it again."