Coyle, 43, who played for Bolton in the mid-1990s, takes over at the Reebok Stadium from Gary Megson who was sacked on December 30.
Bolton are 18th in the 20-team standings and battling against relegation.
Bolton confirmed the appointment on their website with Coyle, who has a 2-1/2 year contract, saying:
"I am absolutely delighted to be back at Bolton Wanderers. I look forward to the opportunity of bringing the good times back to the club for everyone."
Bolton chairman Phil Gartside, who had to pay Burnley compensation for Coyle told the website: "Owen was our number one target and we are naturally delighted that he has returned to the football club as manager.
"He was an inspirational player who leads by example and a great motivator. On behalf of everyone at Bolton Wanderers, I would like to say welcome home."
Coyle's first match in charge will be at home to Arsenal in the Premier League on January 17 following the postponement of their game at Sunderland on Saturday due to the icy weather gripping Britain.
HUGELY POPULAR
Burnley, who are looking for a new permanent manager, have put Steve Davis in temporary charge.
They are 14th with 20 points, just two more than Bolton who have two games in hand, and also face a struggle to stay up.
Coyle was hugely popular at Burnley until agreeing to leave on Monday after taking the club back into the top flight of English football for the first time in 33 years.
However, his move to local rivals Bolton has angered Burnley fans while defender Graham Alexander said now Coyle had left the club he was out of the players' thoughts.
"Come the next game Owen Coyle isn't going to be thinking about us so we can't afford to think about him.
"We've got to think about ourselves. We have played under him but we haven't played for him, we have played for Burnley and that's what we've got to take on.
"The thing we've got to do is play for ourselves, each other, the fans and the people that pay us. That's all we've got on our minds.
"As much as a great job Owen did here it wasn't down to one man. There are a lot of good players in there as well. We have got a lot of quality in that changing room and we will stick together because we have got a great team spirit."
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