Woods' agency, SportsTrust Advisors, announced the move Friday, a few hours after the Seahawks' one-year deal with pass-rusher Ezekiel Ansah became official.
Woods, 32, was among several defensive tackles who visited the Seahawks, according to ESPN's Field Yates, as they looked to add a run-stuffing presence after letting 2018 starter Shamar Stephen leave in free agency. At the owners meetings in March, coach Pete Carroll called that a "clear-cut" area of need, and the only notable addition Seattle made at that position since then was drafting Demarcus Christmas in the sixth round.
Woods, who is listed at 6-foot-4 and 330 pounds, will be the leading candidate to play nose tackle in Seattle's base defense alongside Jarran Reed. The Seahawks' other interior defensive linemen are Quinton Jefferson (who also plays end), Poona Ford, Jamie Meder and undrafted rookies Bryan Mone and Jay-Tee Tiuli.
Woods has made 43 starts and appeared in 111 games since entering the league as a fourth-round pick out of LSU in 2010. He made eight starts last season for the Colts and has played for four other teams, including a two-game stint with Seattle in 2011.
The Seahawks have been busy since Tuesday, the date after which free-agent additions no longer count against the formula for compensatory picks. In addition to Ansah and Woods, they've also signed cornerback Jamar Taylor, fullback Nick Bellore and guard Marcus Martin. The Seahawks are projected to receive the maximum of four 2020 compensatory picks and did not want to lose any of those by signing Ansah or Woods before the May 7 cutoff point.