The two Premier League clubs have been negotiating a compensation deal since Coyle began talks with Bolton following their sacking of Gary Megson last week.
Bolton, who were travelling to London on Wednesday for a Premier League match at Arsenal, have yet to make an official announcement but Kilby made it clear Coyle would be returning to the club where he spent two years as a player in the 1990s.
"It's been a trauma for the club, none of us wanted Owen to go and it was a shock when all this broke," he told Sky Sports News.
"We got Owen to delay his decision 24 hours and put our case strongly but he decided he wanted to go to Bolton.
"Owen has big affection for this club. It's been a fabulous two years for this club. He did say it was only Celtic or Bolton he would leave for.
"He was extremely emotional yesterday saying goodbye to everybody, leaving the club."
Asked if he was surprised Coyle had made what local media were describing as a "sideways move," Kilby said:
"Yes...I fully expected when Owen did move from here he would go upwards from Burnley, not sideways to a team we are fighting a relegation scrap with."
Burnley said first team coach Steve Davis will take charge for Saturday's home league game against Stoke City.
Coyle took over at Burnley in November 2007 when they were in the Championship. The following season he led them to League Cup wins over Arsenal and Chelsea before losing to Tottenham Hotspur in the semi-finals.
Last season, playing attractive, passing football, Burnley reached the play-offs and beat Sheffield United at Wembley to return to the top flight for the first time since 1976.
Coyle, a Scot, turned down the chance to take over Celtic last summer, saying he wanted to see through Burnley's Premier League adventure.
It looked a good decision as they won their first four home games, including a memorable 1-0 victory over Manchester United, but their away form has been dire, leaving them two points above the relegation zone - where Bolton currently sit.
