Pierce joined the Blue Bombers as a free agent in 2010 and made 31 starts over four seasons.
The 31-year-old suffered an undisclosed injury in a 37-14 loss to Hamilton on Aug. 24. He was replaced by Justin Goltz, who led the Blue Bombers past Saskatchewan 25-13 on Sunday before the trade was announced.
"Buck has been a true warrior and a consummate professional during his time Winnipeg and we sincerely thank him for his four years of service to our organization," said acting general manager Kyle Walters in a statement.
Pierce made his CFL debut with B.C. in 2005 and spent five seasons with the Lions before moving to Winnipeg. Pierce, who has struggled with injuries throughout his career, has 1,179 career completions for 15,059 yards and 73 touchdowns against 62 interceptions.
Pierce's best year with the Blue Bombers was in 2011, when he threw for 3,348 yards and 14 touchdowns en route to an eventual Grey Cup loss against B.C. He'll be a backup in B.C., where Travis Lulay is the No. 1 starter.
In return, the Blue Bombers acquired non-import receiver Akeem Foster.
The 26-year-old from Ajax, Ont., joined the Lions in 2010 but made his playing debut a season later. Foster has 61 receptions for 949 yards and nine touchdowns in 32 starts.
"In Akeem, we are getting a veteran Canadian receiver who, at age 26, is still entering the prime of his career," said Walters. "His presence immediately helps upgrade our non-import talent on our roster."