Warburton told the club's website: "Uwe's departure is of course a loss to the club but any such departure is testament and recognition of the hard work and dedication he, his staff and of course the players have displayed over the course of the last two-and-a-half years.
"Uwe leaves the club in an excellent condition and I know that he and I both share the absolute belief that this squad of players can move the club forward to achieve its aims and ambitions.
"I personally want to wish Uwe all the very best in his new role, thank him for his outstanding work and also for his support to me. He is a good friend and will always be welcome to visit us at [Griffin Park] at any time."
Rosler takes up the role after Owen Coyle left Wigan last weekend.