The 45-year-old German leaves the Bees, with whom he was the width of a crossbar away from taking into the Championship last season, and will watch his new side's game with Millwall on Saturday from the stands, starting work on Sunday.
Latics chairman Dave Whelan, who met Rosler on Friday, 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."
Wigan, who were "reluctantly" granted permission to speak to Rosler on Thursday night, moved swiftly to appoint their second manager in the space of six months after Owen Coyle's offer to resign was accepted by Whelan last Sunday following a run of three successive home defeats in nine days.
Whelan has now tasked Rosler, a manager with Norwegian clubs Lillestrom, Viking and Molde before joining the Bees, with reaching the play-offs this season and restoring the club's Barclays Premier League status by the end of the following campaign.
They spent eight seasons in the top flight and won the FA Cup in May just prior to their relegation, so Rosler must win over an expectant support which is also keen for a return to the style of football that earned former boss Roberto Martinez such wide-spread acclaim.
Wigan are 14th in the Championship, nine points adrift of the play-offs, and still in with a chance of making the Europa League's last 32, which is where Rosler's attention must first turn.
After a trip to Millwall on Saturday, Wigan travel to Slovenia this Thursday to take on Maribor needing to win that clash and hope Zulte Waregem lose against group winners Rubin Kazan to ensure their progression.
Rosler's first game in charge at the DW Stadium will come three days later when Coyle's former club Bolton visit in a derby likely to have now taken on extra significance.
Former Manchester City striker Rosler had been with Brentford since June 2011 and twice came close to lifting them into the second tier of English football last term.
Their dreams were first dashed when Marcello Trotta's penalty hit the bar moments before Doncaster grabbed a winner in an unforgettable last-day clash, then a play-off final against Yeovil ended in more heartbreak for the Bees at Wembley.
Rosler's move to Wigan means he will be managing in the Championship this season after all although with Whelan's aspirations, only a quick return to the Premier League will suffice.