The Redskins announced the signing Thursday.
McCoy appeared in four games for the 49ers last season, completing his only pass attempt for 13 yards and rushing for minus-6 yards on six carries. San Francisco acquired McCoy from the Browns on April 1, 2013, along with a sixth-round draft pick in exchange for the fifth- and seventh-round picks.
He was the starter in Cleveland for parts of two seasons, making eight starts as a rookie in 2010 and starting 13 games in 2011. The arrival of rookie quarterback Brandon Weeden, Cleveland’s first-round draft choice in 2012, relegated him to bench duty with the Browns.
McCoy completed 58.3 percent of his passes with the Browns and the team was 6-15 in his 21 starts. He threw for 4,388 yards and 21 touchdowns with 20 interceptions and was credited with one fourth-quarter comeback victory and three game-winning drives in 2011.
He was drafted by the Browns in the third round in 2010 after a dazzling four-year career at the University of Texas during which he threw for more than 13,000 yards and 112 touchdowns.