The Championship club was given permission by St Johnstone to open talks with Coyle after the clubs agreed a compensation package. Coyle, 41, had more than two-and-a-half years remaining on a three-year contract at McDiarmid Park.
"There were some outstanding candidates for the post, but Owen has all the credentials to make a success of his appointment," said Burnley chairman Barry Kilby.
"He is hungry for the opportunity to manage in England after an impressive start to his career in Scotland. The fact that Scotland manager Alex McLeish took time out from preparing his country's huge Euro 2008 qualifier against Italy to sing Owen's praises shows he has the support of some top people. I am sure the fans will join me in welcoming Owen to Turf Moor and wishing him every success."