Mackay has been out of work since being dismissed by Cardiff City last December after a fall out with the Welsh club's owner Vincent Tan.
The 42-year-old Scot was on the verge of taking over at Crystal Palace in August before he was reported to the Football Association over text messages he exchanged with then Cardiff head of recruitment Iain Moody, which he admitted were "disrespectful of other cultures".
Wigan have now given Mackay an opportunity to resume his managerial career as successor to Rosler, who paid the price for a poor start to the season when he was relieved of his duties last week.
The Lancashire club's chairman Dave Whelan is backing the former Scotland international to take Wigan back into the Premier League, having achieved that feat with Cardiff.
"He is the man to lead us back into the Premier League, I am convinced of that having met him and discussed the demands of the job ahead of him," Whelan told Wigan's official website.
"He has led a team out of the Championship before and he knows this league inside out having played and managed in it."
Whelan is aware that Mackay's appointment could be viewed as controversial, but believes he deserves another chance.
"I know that this appointment will draw criticism in some quarters but we go into it with our eyes open and we have nothing to hide on this subject." he added.
"Malky made a mistake, he knows that, we know that and we have discussed this issue at length face to face. He apologised publicly for what happened at the time and has paid for what he did in terms of the bad publicity he has received since and will no doubt continue to suffer in the future."
Wigan are languishing in the relegation zone ahead of their clash with high-flying Middlesbrough on Saturday.
