Financial terms of the one-year contract were not disclosed.
Fullmer, 28, spent the past two years with the Anaheim Angels. His 2003 season was cut short by a ruptured patella tendon. He underwent surgery on July 1 and is expected to be ready for spring training.
"We have always liked Brad," said Texas General Manager John Hart. "He is a hard-nosed player who has played on a world champion. He is a middle-of-the-order bat and we are excited to have him."
Fullmer batted .305 with nine homers and 35 RBI last year before the season-ending injury, which put him on the disabled list for the first time in his career.
The career .328 hitter with the bases loaded had his best season in 2000, batting .295 with 32 homers and 104 RBI in 133 games for Toronto.
Notable deaths of 2014 [PHOTOS]