This signing, anticipated since Veldheer's visit with the Pats last week, is expected to come after Tuesday's compensatory pick deadline, which means the team will be able to sign a player without it affecting the compensatory pick formula (as the Patriots are projected to receive two third-round picks and two sixth-round picks).
The news was first reported by NFL Network.
Veldheer, who turns 32 next month, provides veteran insurance behind 2018 first-round draft pick Isaiah Wynn (who is coming off an Achilles tear) and Yodny Cajuste (who is coming off a calf injury). The Patriots lost two offensive tackles in free agency -- starter Trent Brown (Oakland) and backup LaAdrian Waddle (Buffalo).
Veldheer, who was acquired by the Denver Broncos last March in a trade with the Arizona Cardinals, was a steadying influence for a Denver offensive line beset by injuries and lineup changes during the 2018 season.
He started 12 games at right tackle for the Broncos, but he also didn't escape the team's rash of injuries. The 10-year veteran left one game with a concussion and missed four games with a knee injury.
He also has started at left tackle in his career, and he had one start at center while with the Oakland Raiders earlier in his career.
The 6-foot-8 Veldheer was a bit of a late bloomer. A lightly recruited prep player in Grand Rapids, Michigan, Veldheer started for four seasons at Division II Hillsdale College before the Raiders made him a third-round pick (69th overall) in the 2010 draft.
ESPN's Jeff Legwold contributed to this report.