The news comes via USA Today's Mike Garafolo, who said Clemens agreed to a league-minimum contract.
When Bradford sat with a high ankle sprain in 2011, Clemens started the last three games. The Rams lost all three, getting outscored 81-40 as Clemens posted a 73.8 passer rating.
Last season he was picked off on one of his three pass attempts.
Clemens' most significant action came in 2007 with the Jets. In 10 games, he completed 52 percent of his throws for 1,529 yards and five touchdowns, with 10 interceptions.