BEREA, Ohio -- The Cleveland Browns have signed third-string quarterback Austin Davis to a two-year contract extension through 2017.

The deal is for $4.137 million and includes a $500,000 signing bonus and has $600,000 in total guarantees, a source told ESPN's Field Yates.

The Browns signed Davis, who went 3-5 as a starter last season with St. Louis, to a one-year deal on Sept. 7, two days after he was waived by the Rams. He hasn't played with Cleveland and is currently behind both Josh McCown and Johnny Manziel on the depth chart.

Davis came off the bench in St. Louis after injuries sidelined Sam Bradford and Shaun Hill. Davis passed for 2,001 yards and 12 touchdowns.

The Associated Press contributed to this report.