He immediately saw his new side get a home draw as the bid to retain the FA Cup, with MK Dons the visitors to the DW Stadium in January.
Rosler replaces ex-Burnley and Bolton boss Coyle won just seven of his 23 matches in charge, leaving "by mutual agreement" following a 3-1 home defeat by Derby last month.
The Latics were granted permission to speak to Rosler, 45, on Thursday and he has agreed to move to the DW Stadium after talks with chairman Dave Whelan.
The German watched Saturday's match at Millwall from the stands, before officially starting work today..
"Uwe is one of the brightest young managers in the Football League and his ambition is to manage in the Premier League," Whelan said.
"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."
Whelan has agreed a compensation fee with Brentford to bring in Rosler as the successor to Owen Coyle, who left Wigan on Monday less than six months after he replaced Roberto Martinez as manager.
The former Manchester City striker leaves Brentford fourth in League One, having won the division's manager of the month award for November, and with the club celebrating being given the go-ahead to build a new 20,000-seater stadium. Ironically, Brentford lost to Carlisle in the FA Cup on Saturday.
Wigan's recent managers
Owen Coyle: June 2013 - December 2013
Roberto Martinez: June 2009 - June 2013
Steve Bruce: November 2007 - June 2009
Chris Hutchings: May 2007 - November 2007
Paul Jewell: June 2001 - May 2007