Keenum beat out rookie first-round pick Dwayne Haskins and fellow veteran Colt McCoy for the job. He was 16-for-30 for 213 yards with one touchdown over the first three games of the preseason.
The Redskins visit the Philadelphia Eagles on Sept. 8 in the season opener.
Alex Smith started for the Redskins last season but complications during and after surgery to repair a broken leg make his return this season extremely unlikely.
McCoy, who turns 33 the night of the NFL regular-season opener between the Chicago Bears and Green Bay Packers , had surgery to repair a broken right leg. He's been in Washington since 2014, but made only six starts in those five seasons. He had just 41 pass attempts in the past four years and has been unavailable in the preseason.
Haskins, the 15th overall pick out of Ohio State, completed 22 of 41 passes with one touchdown and two interceptions in three preseason games. He was also sacked five times.
--Field Level Media