The deal was announced Thursday night. Burns, who is making $875,000 this year, will earn $3 million next season, $3.4 million in 2009-10, $3.8 million in 2010-11 and $4 million in 2011-12.
Burns, 22, has four points (3-1) and a plus-6 rating in 10 games this season.
"The effort Brent has given to improving himself as a player is evident to the point that he is becoming an impact player in our lineup," Wild general manager Doug Risebrough said in a statement. "This is recognition of that effort and of his potential."
Burns has 15 goals and 36 assists in 195 career games with the Wild, who selected him in the first round (20th overall) of the 2003 draft.