Denver sent a sixth-round selection in the 2018 draft to the Cardinals in exchange for Veldheer, who became expendable when the Cardinals signed offensive linemen Andre Smith and Justin Pugh in free agency.
Veldheer, 30, has played eight seasons in the NFL since the Oakland Raiders picked him in the third round of the 2010 draft.
The 6-foot-8, 321-pound Veldheer spent four seasons with Oakland and four with Arizona, starting 101 of 106 regular-season games. He missed 11 games over the past two seasons after starting all 32 in his first two seasons with the Cardinals.
Veldheer played both tackle spots for Arizona in 2017, although he has seen most of his time at left tackle throughout his career. He is expected to start at right tackle for the Broncos.