Casey, 30, had 44 tackles, 10 quarterback hits, five tackles for a loss, five sacks, two fumble recoveries and a forced fumble in 14 starts last season for the Titans.
The nine-year veteran has gone to five consecutive Pro Bowls. Casey signed a four-year, $60.4 million contract extension with the Titans in 2017.
The trade comes after the Broncos agreed to trade for Pro Bowl cornerback A.J. Bouye on March 3. Denver will send a fourth-round pick in the 2020 NFL Draft to the Jacksonville Jaguars as part of that swap.
The Broncos also have agreed to sign backup quarterback Jeff Driskel and guard Graham Glaskow this off-season.
Casey has an $11.85 million base salary in 2020, with $5.45 million of that salary guaranteed this weekend. He is signed through 2022.