Both are signed through the 2017 season.
Elimimian made CFL history in 2014, registering a league-record 143 tackles then becoming the first full-time defensive player to capture its outstanding player award. He was also named the most outstanding defensive player.
"I've never been more proud to be a Lion and I am very happy to be part of this organization moving forward," Elimimian said in a statement. "I want nothing more than to put on that orange jersey and help win championships for our fans.
"It's also very special to be doing this with Adam. Playing alongside him is like playing beside your brother and it means the world to me that we are able to do this extension together."
Elimimian, heading into his sixth season with the Lions, has registered 430 total tackles, leaving him third in club history.
"When you can secure two of our league's best defensive players with long-term contracts, it's a very special day," Lions' vice-president of football operations and GM Wally Buono said. "Solomon and Adam are impact players who not only make our defence extremely difficult to play against, they also bring the kind of leadership needed to form the foundation of a championship team."
Bighill enters his fifth season with B.C., having recorded 280 tackles, 24 sacks, 62 special-teams tackles, six forced fumbled and six interceptions in 63 regular-season appearances.
"I'm thrilled to sign this extension and know that I am a Lion through 2017," said Bighill. "Playing football in B.C. with the core group we have here means you have an opportunity to win a Grey Cup every season and that's our ultimate goal.
"Knowing I get to do that with Solomon makes it that much better."