The pair signed three-year contracts at the Reebok Stadium as they make the step up from Championship to Premier League football.
"Both Chris and Tyrone are top players, and have shown that they have the ability to compete successfully at the highest level," Bolton manager Owen Coyle told the club's official website.
Eagles, 25, and Mears, 28 - who both played under Coyle when he was manager at Burnley - join Nigel Reo-Coker in signing for Bolton.
"I have worked with them both before and know what they will bring to the club in terms of character and commitment, and along with Nigel Ro-Coker we have added real quality to the club," Coyle added.
Bolton continue their pre-season preparations at Newport County on Saturday.