Marsh was the eighth player chosen in the round, the 108th pick overall.
"So happy to be a part of the seahawks organization! Can't wait to get to work towards this next super bowl!" Marsh posted on Twitter.
Last season, the 6-foot-4, 252-pound Marsh had 10-1/2 tackles for losses, including six sacks.
Marsh was the third Bruins player selected in the draft. Linebacker Anthony Barr was chosen ninth overall by the Minnesota Vikings. Offensive lineman Xavier Su'a-Filo was drafted by the Houston Texans with the first pick of the second round, the 33rd selection overall.
Marsh, who played at Westlake Village Oaks Christian High, was a two-year starter for the Bruins.