Norwood finished the 2014 regular season tied for second in the CFL with a career-high 13 sacks.
He added 48 defensive tackles and two forced fumbles en route to being named an East Division all-star.
In 32 regular season games, the South Carolina product has compiled 93 defensive tackles, 17 quarterback sacks, seven tackles for a loss, and three forced fumbles with the Ticats.
"We're excited to have Eric in Black and Gold for years to come, as he has been an integral part of our defence over the last two seasons and has shown he is one of the league's premier pass rushers," Ticats general manager and head coach Kent Austin said in a statement.
Norwood, originally signed with the Tiger-Cats on July 2, 2013, after previously being selected in the fourth round (124th overall) by the NFL's Carolina Panthers.