Former Scunthorpe and Grimsby boss Laws took up the role at Turf Moor following his departure from Sheffield Wednesday.
Coyle said: "I rang Brian the other day when he was appointed. I know him well, he is someone I have a lot of time for.
"He knows he has inherited a tremendous group of players. He is a good manager and a good man. I wish him well.
"Everyone knows my feelings for Burnley and I want nothing but the best for the club despite what some people are saying."
Coyle is relishing the challenge that lies ahead tomorrow when they face Arsene Wenger's Arsenal at the Reebok Stadium.
He said: "It will be emotional as it is my first game in charge and I will feel a sense of pride as well. If I wasn't nervous there would be something wrong.
"I feel privileged to be Bolton's manager and excited about what lies ahead. You want the ball rolling. We will try and earn some points.
"It is a game to look forward to against a team that is the role model for any young manager. You look at the way Arsene Wenger has built that club and the style of play. I am a big admirer of them."