The Redskins parted ways with former top pick Robert Griffin III this week.
McCoy, 29, spent the past two seasons mostly in a backup role with the Redskins.
He played in five games with four starts in 2014, completing 71.1 percent of his passes with four touchdowns and three interceptions. He averaged 8.3 yards per pass attempt. McCoy lost his job because of a season-ending neck injury in Week 15.
McCoy re-signed with Washington in hopes of competing for the starting job. But the Redskins opted for Cousins, and McCoy served as the backup all season. He ended up playing in two games, completing 7 of 11 passes for 128 yards and one touchdown.
McCoy has also played for Cleveland and San Francisco. The former third-round pick from Texas has played in 35 career games with 26 touchdowns and 23 interceptions.
ESPN NFL Nation reporter John Keim contributed to this report.