"We are trying to bring real quality players to the football club and in Remco we have undoubted quality," Coyle said after completing the deal.
"He is a powerful lad who is very good on the ball and a very capable player. When he went to PSV Eindhoven from Vitesse Arnhem I think they played €3 million for him.
"He is still only just turned 29, so he will be a tremendous addition to the squad and I honestly think the next three years will be his best years. Hopefully we will benefit from that. I think it will be an exciting time when Burnley fans see him and I'm absolutely delighted to have him on board."
There were other clubs, and bigger clubs (Cardiff are not included in that) chasing the player and Coyle added: "We worked very hard to get Remco. We have been in negotiations for several weeks now and he had a lot of interest from a number of clubs, so we are delighted to nail this one down.
"He's a defensive type of midfield player who I feel will enhance our team. Last year we were very committed to going forward and we will do that again this year, but we don't want to leave ourselves wide open and I think Remco will patrol that area and give us a bit of protection.
"Equally he is 6ft 1ins, he can pass a ball and put his foot in where it hurts, so he's a terrific addition. He will join us now going to America, so that gives him a good chance to bond with his new team mates.
"He has played at the top level throughout his career in Holland and I am sure he will have no trouble adjusting and complimenting everything we are trying to do at this football club."