With the "interim" tag removed from his title, Burke officially becomes the Bombers' 29th head coach since the team's inception in 1930.
In a statement released Thursday, Mack said the players have great respect for Burke, adding that the coach now has a full off-season to implement his own system and style of coaching.
"I am more than ecstatic to be the head coach of the Winnipeg Blue Bombers," Burke said in the statement.
"I've waited a long time for this and I look forward to having the opportunity to lead this football team. I believe in where this organization is headed and I can’t wait to get started on doing what I can to improve on our record from this season and bring the people of Winnipeg and fans of this team back to the Grey Cup."
Burke took over the position on an interim basis on Aug. 25 after then-head coach Paul LaPolice was fired.
The Bombers are coming off one of their worst seasons in recent years, with a 5-12 record so far, and have failed to make the playoffs.
Pressure on Mack
Mack has felt the pressure from thousands of fans who joined the "Fire Joe Mack" movement on Facebook and Twitter earlier this season to demand his dismissal.
But the Bombers' board of directors chairman, Bill Watchorn, backed his GM in September, saying the board has confidence in Mack, despite the growing public backlash.
Now, Mack is backing up his coach.
"Tim has done a great job at leading this football team since taking over the position in August and our players have shown a great deal of respect for him and his coaching style," he said.
“We believe that by naming him head coach now, he will have a full offseason to implement his own system and style of coaching and will give us a head start on bettering our team for next season.”
Burke first joined Winnipeg as defensive coordinator and defensive backs coach in 2011, leading a unit that finished first in 12 defensive categories to an east division championship and an appearance in the Grey Cup.
Before coming to Winnipeg, he spent three seasons with the Montreal Alouettes in the same role, where he made three straight Grey Cup appearances, winning back-to-back games in 2009 and 2010.
Other CFL experience includes three seasons with the Calgary Stampeders as their defensive backs coach before being promoted to interim defensive coordinator in 2007.