Speculation has become reality, as NFL Network learned Sunday night that Cooley has agreed to sign a deal with the team.
Cooley is scheduled to undergo a physical Monday. His signing will become official after that, barring any unexpected last-minute snags.
"It's going to happen," a source told The Washington Post.
Cooley wouldn't comment, telling The Post it would be premature to do so.
Cooley was released during training camp, ending an eight-year run with the team. He said last month it was unlikely he'd come back to the Redskins unless Davis or backup tight end Niles Paul suffered a significant injury.
Cooley, 30, owns the franchise record for receptions for a tight end, but expect him to have a lesser role in his second go-around with Washington. Paul should get every opportunity to stick in the starting lineup.
Follow Dan Hanzus on Twitter @danhanzus.