The move made the league transaction wire.
The Patriots selected Woodard, 23, in the seventh round last spring at No. 230 overall. The former University of Memphis interior offensive lineman retired before the start of his first NFL training camp. He was later reinstated to the active roster from the retired list on April 7.
Woodard started 52 games during his college career between left guard, right guard and center. The 6-foot-2, 291-pound blocker earned first-team and second-team All-American Athletic Conference honors for the Tigers between his junior and senior seasons.
New England’s current center depth chart includes re-signed team captain David Andrews along with the returning Ted Karras, Marcus Martin and Najee Toran.
The 90-man offseason roster now stands at 76 with the 2021 NFL draft under two weeks away.
A total of 10 selections are scheduled for the Patriots’ war room, beginning at No. 15 overall and continuing up through No. 242 overall.