Holcomb, who spent last season backing up Jeff Garcia in Cleveland, will play behind sophomore J.P. Losman. The Bills released Bledsoe last week and he quickly signed with the Cowboys.
Holcomb made four appearances in 2004, including two starts. He finished 59-of-87 for 737 yards and seven touchdowns, with five interceptions.
Normally free-spending Washington declared itself done for now after signing center Casey Rabach and wide receiver David Patten.
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