Career
He was signed by the Broncos as an undrafted free agent in 2014. He played college football at Colorado State University. Barrett started playing college football at the University of Nebraska Omaha in 2010.
After the school eliminated its football program, he transferred to Colorado State.
Since Barrett was transferring from a school that cut its program, he was eligible to play immediately instead of having to sit out a year. After going undrafted in the 2014 NFL Draft, Barrett signed with the Denver Broncos.
After being waived for final roster cuts before the start of the 2014 season, the Broncos signed him to their practice squad on August 31, 2014. After the 2015 NFL preseason he made the final 53 man roster.
He finished the preseason with the most sacks of any player.
In week 6 of the 2015 season Barrett had his first NFL start after Demarcus Ware suffered a back injury. Barrett played in Super Bowl 50, and was evaluated with a concussion and returned to finished the game after he passed the concussion protocal. The Broncos defeated the Carolina Panthers 24-10.