Mike Klis of 9News first reported the news.
Tennessee will receive a seventh-round pick in exchange for the 30-year-old, per Ian Rapoport of NFL Network.
As Rapoport noted, "Tennessee had quietly been open to offers for Casey."
Casey has made the Pro Bowl in each of the last five seasons, totaling 51 sacks in his nine years with the Titans.
Despite his on-field impact, his salary helped force the trade for minimal return:
John Glennon @glennonsports
Told #Broncos will be taking all of Casey's future $$: --Casey due to count $13.4 mil against cap this yr, $13.9 next year and $13.9 in 2022. --$5.45 million of 2020 salary would have been gtd on 3/22, per @spotrac.com. --Broncos' willingness to take $$ explains 7th-rd pick only.
The Titans could have a numbers crunch after reportedly signing quarterback Ryan Tannehill to a four-year extension worth $118 million. The team also used the franchise tag on Derrick Henry, which will be worth $10.3 million in 2020 if the two sides don't agree to a new deal.
That left Casey as an odd man out even though he totaled 44 tackles and five sacks from the interior defensive line last season.
He was a key part of the defense that held the New England Patriots and Baltimore Ravens to a combined 25 points in two upset wins in the playoffs, leading the Titans to a surprise run to the AFC Championship Game.
Denver will hope his skill set further improves a defense that finished last season 10th in the league in points allowed and 12th in yards allowed.
With both Derek Wolfe and Shelby Harris entering free agency, Casey provides much-needed help on the defensive line.
The Broncos reportedly traded fullback Andy Janovich to the Cleveland Browns for a 2021 seventh-round pick Tuesday, per Klis. The team essentially flipped a fullback who wasn't going to be used under new offensive coordinator Pat Shurmur for a potentially dominant defensive tackle.