Rosler was given permission by Brentford to speak to Wigan following the departure of Latics manager Owen Coyle, who left by mutual consent on Monday.
The two clubs have since thrashed out a compensation fee and Rosler will attend Wigan's Championship clash at Millwall on Saturday before he is officially unveiled on Monday.
Latics chairman Dave Whelan welcomed the arrival of Rosler, who had an impressive spell at Brentford in his first managerial job in England.
Whelan said: "Uwe is one of the brightest young managers in the Football League and his ambition is to manage in the Premier League.
"He impressed me enormously when I spoke to him, he has a strong philosophy about how to play the game and has a desire to shape all aspects of the long term future of the club.
"I think he can and will achieve great things here at Wigan Athletic."
The German guided the Bees into a ninth-placed finish in League One in his first season in charge and they narrowly missed out on promotion last term after losing to Doncaster in their final game and then going down to Yeovil in the play-off final.
He had steered Brentford into fourth place in the table this season and sporting director Mark Warburton insists he leaves with the club's best wishes.
Warburton said: "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 GP at any time."
Assistant manager Alan Kernaghan and first team coach Peter Farrell will take charge of Brentford for the FA Cup second-round trip to Carlisle.