Vannett, 28, appeared in 15 games last season but played only 34 percent of the offensive snaps. He made 14 receptions for 95 yards and a touchdown.
He was due to make $2.68 million with the Broncos in 2021.
The Seahawks made Vannett a third-round choice in 2016. Seattle traded him to the Steelers in 2019, and Vannett finished that season with the club before signing a two-year deal with Denver last April.
Vannett has 75 career receptions for 686 yards with five touchdowns in 70 games.