"He was an inspirational player who leads by example and a great motivator and, on behalf of everyone at Bolton Wanderers, I would like to say welcome home."
Last year Coyle led Burnley back to the top flight for the first time in 33 years.
In a statement on the club's website Burnley said: "The officials of Burnley Football Club would like to place on record their thanks to Owen for his services to the club and contribution to our success."
Coyle had signed a 12-month extension to his three-year Burnley contract in the summer and he will not have long to wait before renewing acquaintances - his third game in charge sees Bolton host Burnley, on Tuesday 26 January.
Former Bolton boss Gary Megson was sacked on 30 December with Bolton 18th, two places off the bottom of the Premier League.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.