Per Klis, Denver would use Montgomery at center and have Manny Ramirez shift over to replace Zane Beadles at left guard.
Montgomery was released by Washington on Friday in a cap-related move; the team is shifting former Denver draftee Kory Lichtensteiger over to take his place.
Most of the Maine native's first four seasons were spent at guard, but he shifted over to center in 2011 when Lichtensteiger suffered a knee injury.
The Va Tech alum turned 31 last month and has played in 90 career games (63 starts), grading out at +4.8 over 1,172 snaps in 2013.
In 2012, Montgomery graded out at +21.8 over 1,112 snaps; he has missed only six snaps over the past three seasons, all during one 2012 game.