Clark, 25, hampered by a dislocated left forearm last season, played in 11 games for the Miami Dolphins, catching just two passes for 42 yards.
Despite his off year, Clark should fit in with the Bears, who struggled for consistency at the tight end position. Chicago used John Allred, Fred Baxter and John Gilmore at tight end.
Clark spent his first three seasons with the Denver Broncos before getting waived last August. In 2001, he had a career-high 51 receptions for 566 yards and six touchdowns.
The Bears on Saturday also re-signed tight end John Davis and fullback Stanley Pritchett to one-year contracts.
Davis played in 10 games last season, including eight starts, finishing with 20 receptions for 193 yards and three touchdowns. In 16 games, Pritchett registered 19 receptions for 165 yards and a touchdown.