The former East Germany international had been at Brentford and will begin work at the DW Stadium on Monday, after the clubs have agreed a compensation package.
Rosler, who has also been managed Lillestrom, Viking and Molde previously, will watch Wigan at Millwall on Saturday from the stands, with Graham Barrow in temporary charge.
He leaves Brentford fourth in League One, with Wigan chairman Dave Whelan stating that Rosler can achieve "great things" in his new role.
"Uwe is one of the brightest young managers in the Football League and his ambition is to manage in the Premier League," he said in a statement on the club's website.
"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."
Rosler takes over at Wigan following the sacking of Owen Coyle on Monday, with the FA Cup holders 14th in the table.
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