Right-back Mears, 28, and former Manchester United midfielder Eagles were both brought to Burnley by Owen Coyle, but were unable to help them survive in their inaugural campaign in the Premier League in 2009-10 or achieve an instant return last season.
A club statement said: "Burnley Football Club had hoped to persuade the players to sign extensions to their present deals.
"However, with the players expressing their desire to immediately return to the Premier League, and effectively able to leave Turf Moor for free next summer, Burnley Football Club regrettably has accepted this offer from Bolton.
"Mears and Eagles will not take part in the Clarets' pre-season friendly at Torquay today, as they look to discuss personal terms with Wanderers.
"The funds from Eagles and Mears' expected departures will be used to strengthen the squad, with further transfer developments expected early next week.
"Burnley Football Club will make no further comment at this time."