Keenum was battling for the starting job with rookie Dwayne Haskins, the club's first-round pick in 2019.
"Case has come in here and picked up the offense extremely well, had great confidence and command over the team - they both have," Gruden told reporters. "At the end of the day, I think we have great confidence Case can lead us to a win against Philadelphia."
Keenum, who was traded from Denver to Washington in March, started all 16 games for the Broncos last season. He completed 62.3 percent of his pass attempts for 3,890 yards and 18 touchdowns against 15 interceptions.
"The experience factor is something you really lean upon," Gruden added.
The 2018 campaign was disappointing for Keenum, who was met with high expectations after leading the Minnesota Vikings to the NFC Championship game the year prior. He completed 67.6 percent of his passes for 3,547 yards and 22 touchdowns with seven interceptions in 2017.
Neither Keenum nor Haskins set the world on fire during preseason, but overall, the veteran was more effective, specifically when it came to ball security.
The Redskins were forced to improve their quarterback situation this offseason after Alex Smith suffered a career-threatening leg injury last year.