Midfielder Eagles, 25, and defender Mears, 28, have both agreed three-year contracts.
"Both Chris and Tyrone are top players and have shown that they have the ability to compete successfully at the highest level," said manager Owen Coyle, who knows the players from his time as boss of the Clarets.
"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 Reo-Coker, we have added real quality to the squad."
The pair become Coyle's third and fourth signings of the summer after the arrivals of Darren Pratley and Reo-Coker.
"I know that it is a good squad so the challenge for me will be to work hard and then look to contribute," said Eagles.
"I am an attacking midfielder and I will certainly be looking to chip in with some goals."
Mears added: "I'm really looking forward to working with a manager I've worked with before and playing in the Premier League.
"From the outside looking in, this has seemed like it is a club going in the right direction.
"It wasn't a difficult decision at all. I know exactly what the manager expects from his players and I'm more than ready for it."
Source: PA
Source: PA