The six-foot-five, 325-pound Toronto native was named an OUA first-team all-star and second team All-Canadian with the Gryphons last year and arrives in Hamilton after the Ticats acquired the pick from the Montreal Alouettes in the 2018 Johnny Manziel trade.
Woodmansey, 22, played 32 games, including 28 starts at guard, from 2016 to 2019 and played for the West team in the U Sports East-West Bowl.
With the eighth overall selection, Hamilton chose North Dakota defensive lineman Mason Bennett.
The six-foot-four, 235-pound native of Winnipeg recorded 39 tackles and 5.5 sacks with the Fighting Hawks in 2019, and totaled 128 tackles and 20 sacks in his four year collegiate career.
Bennett was selected to the Associated Press All-American third team in 2019.
The Ticats took Acadia linebacker Bailey Feltmate, 22, in the second round of the draft, 17th overall.
Feltmate was an AUS all-star in 2017, 2018 and 2019 and the AUS Defensive Player of the Year in 2017 and 2019 with the Axemen.
The Tiger-Cats stayed close to home with their third round selection, 27th overall, when they took Waterloo receiver and Hamilton native Tyler Ternowski.
The 22-year-old Sir Allan MacNab graduate made 164 receptions for 2,949 yards and 26 touchdowns during his four years with the Warriors and earned OUA First-Team all-star honours in each of his last three seasons.
Ternowski was a U Sports First-Team All-Canadian in 2018 and 2019.
In round four, Hamilton selected UBC defensive back Stavros Katsantonis, a First-Team All-Canadian in 2016, 2017 and 2018.
The Bakersfield, California native was handed a four-year ban in U Sports after testing positive for a banned substance (prohibited anabolic agent) last spring but he is allowed to play in the CFL in 2020.
McMaster offensive and defensive lineman Joseph Bencze was taken by Hamilton in the fifth round, 45th overall, one of four Marauders drafted on Thursday.
The 23-year-old Bencze, who is projected to play offensive line in the CFL, recorded 26.5 defensive tackles and two sacks from 2016-2019 at Mac.
Hamilton went back to UBC with their sixth round selection, 54th overall, by taking defensive back Jean Ventose, who made 31 total tackles and one interception with the Thunderbirds in 2017 and 2018.
Ventose, 24, spent the 2016 season with the Calgary Dinos.
The Tiger-Cats made UCLA kicker JJ Molson their seventh round selection, 63rd overall.
In four seasons with the Bruins, the Montrealer converted 51 of his 74 field goal attempts (69%) and earned the Tommy Prothro Award for outstanding special teams play in 2018.
With their last draft pick in the eighth round, 72nd overall, Hamilton selected UBC long snapper Tom Schnitzler.
The 24-year-old from Saskatoon made 16 appearances on the defensive line over two seasons with UBC where he recorded 45 total tackles and three sacks.
The B.C. Lions acquired the No. 1 overall selection by trading their third and 12th overall picks to the Calgary Stampeders, who also shipped their 15th overall pick to B.C.
The Lions used the pick to take East Carolina linebacker Jordan Williams.
The Toronto Argonauts selected Virginia receiver Dejon Brissett second overall, Calgary took Southeast Louisiana defensive end Isaac Adeyemi-Berglund at No. 3, and the Edmonton Eskimos grabbed Buffalo offensive lineman Tomas Jack-Kurkyla with the fourth overall pick.
The Ottawa Redblacks used the sixth overall pick to take Laval defensive back Adam Auclair, the Saskatchewan Roughriders chose University of Saskatchewan offensive lineman Mattland Riley seventh overall, and Toronto picked Regina offensive lineman Theren Churchill with the final selection of the first round.