He won three Grey Cup championships, two with the Calgary Stampeders, in 1998 and 2008, having spent 10 years of his career with them, and one with the Ottawa Redblacks in 2016.

While playing in the CFL, he was also a member of the Saskatchewan Roughriders and Hamilton Tiger-Cats and spent time in the NFL with the Bears and Green Bay Packers.

He had his first, limited playing time in 1998 in relief of Jeff Garcia and Dave Dickenson, while dressing for all of the Stampeders' games.

While his passing was quite poor he showed better than average running ability for a quarterback, finishing the 2002 season with 15 rushes for 104 yards.

In the off-season Burris rejected the Roughriders' contract offer in order to re-join the Calgary Stampeders.

In 2005, he took the Stampeders to the Western Semifinal, where they lost at McMahon Stadium to Ricky Ray and Jason Maas of the Edmonton Eskimos.

In 2008, Burris won his first championship as a starter, leading the Calgary Stampeders to a 22–14 Grey Cup victory, over the host Montreal Alouettes.

Looking for revenge against his play-off nemesis, Burris lost to the Roughriders for the fourth time in the post season, 20–16.

Burris returned to quarterbacking the Calgary Stampeders in the second half of the Western Conference Semi Finals against the Edmonton Eskimos.

Burris was unable to lead a second half comeback throwing only 7 completions in 15 attempts with 0 touchdowns, having to settle for multiple field goals.

The Stampeders seemed ready to move on and hand the starting job to Drew Tate while Burris had stated that he did not want to be a backup quarterback.

The Calgary Stampeders confirmed on January 3, 2012, that they had traded Burris to the Hamilton Tiger-Cats for quarterback Kevin Glenn and offensive lineman Mark Dewit.

Unfortunately, the Tiger-Cats defense struggled, giving up an average of 32 points per game, which resulted in the team falling to 6–12 and missing the playoffs.

Burris led the Tiger-Cats into the post-season with a record of 10–8, they defeated the Montreal Alouettes and then the Toronto Argonauts, but ultimately lost to the Saskatchewan Roughriders in the 101st Grey Cup game.

With the addition of offensive coordinator, Jason Maas, and several key free agent signings, Burris experienced a renaissance season.

[8] Additionally, Burris finished the 2015 season as the league leader in passing yards and completion percentage.

In the Eastern Final, Burris lead the Redblacks over his old team, the Tiger-Cats, personally advancing to the Grey Cup for the second time in three seasons.

[9] Burris left the 2016 season opening game in the third quarter after injuring the pinky finger on his throwing hand.

Following their first round bye Burris led the Redblacks to an East Division Final victory over the Edmonton Eskimos in a snowstorm, advancing the team to its second consecutive Grey Cup game.

[16] On January 19, 2017, it was reported that Burris was leaning towards retirement, citing the desire to spend more time with his wife and help raise their children; while at the same time wanting to play in 2017 to help Ottawa win back-to-back championships at the 105th Grey Cup in Ottawa.

[19] On February 21, 2017, Burris began his broadcasting career and joined CTV Morning Live Ottawa as one of the show's hosts.

2022 saw the Jaguars made a large turn around on offense, spurred by the development of second year quarterback Trevor Lawrence and a breakout season by WR Christian Kirk.

After not being retained by the Jaguars for the 2023 season, Burris joined the Los Angeles Rams for training camp in 2023 as a tight ends coach.