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, a Scot, turned down the chance to take over Celtic last summer, saying he wanted to see through Burnley's Premier League adventure.
