The nine-year CFL veteran spent the last three seasons with the Roughriders. He started 17 of 18 games last season and was named the team's top offensive lineman.
"This is a player with great experience in the CFL," Blue Bombers general manager Kyle Walters said in a release. "He is a tough, hard-nosed football player and we are excited to bring him into the Bombers organization."
Picard, a 32-year-old native of Sainte-Foy, Que., has played in 137 career regular season games. He was originally drafted by the Blue Bombers in the third round of the 2006 CFL Draft and spent three seasons in Winnipeg before joining the Toronto Argonauts.
He was an East Division all-star with the Argonauts in 2011.
The Blue Bombers also re-signed defensive back Demond Washington on Tuesday. He was scheduled to become a free agent next month.
Washington had 70 defensive tackles last season along with four special teams tackles, one fumble recovery and one touchdown. He also had nine kickoff returns for 396 yards, including a 96-yard runback for a TD in Week 2.
The Roughriders, meanwhile, also released Canadian linebacker Tristan Black and re-signed Canadian receiver Alex Anthony and Canadian linebacker Ryan Wellman.