Burnett spent the past three seasons with the Edmonton Eskimos, registering 122 tackles, three special-teams tackles, eight interceptions, 11 pass knockdowns and one fumble return for a touchdown in 39 games.
He was released by the Eskimos last week after a frustrating 2014 season that saw him suit up for just five games because of leg injuries.
Burnett led the CFL in 2012 with six interceptions, including two returned for touchdowns, and was named a West Division and CFL all-star.
The 28-year-old University of Central Florida product has also returned 85 punts for 731 yards and 40 kickoffs for 804 yards over his career.
"Joe is a good and versatile athlete with experience in both the CFL and the NFL," Stampeders coach and general manager John Hufnagel said in a statement. "He has tremendous ball skills, which has allowed him to be a playmaker on defence. I look forward to seeing him compete at training camp."
Burnett joined the Eskimos practice roster in 2011 and made his CFL debut in 2012. He was drafted in the fifth round (168th overall) by the Pittsburgh Steelers in 2009 and appeared in 15 NFL games. He was later signed by the New York Giants and also played with the Arena Football League's Jacksonville Sharks.
"I'm extremely excited for the opportunity and chance to be a part of a tremendous organization — the 2014 Grey Cup championship team," Burnett said in a statement.