ESPN.com's Jerry Crasnick previously reported Papelbon requested his release from the Nationals.
The 35-year-old's role with the Nationals significantly diminished in recent weeks after the team acquired Mark Melancon before the trade deadline.
Chelsea Janes of the Washington Post noted the move makes sense for both the Nationals and Papelbon because the team wanted to open up a roster spot—it brought up minor league pitcher Reynaldo Lopez—and Papelbon wanted to pitch in high-leverage situations.
ESPN's Sarah Langs provided another practical reason for why the Nationals would want to get rid of Papelbon:
If Papelbon wants to pitch in late-game situations again, it likely won't come with a playoff contender. He has been awful in Washington this season with a 4.37 ERA, 37 hits allowed, 14 walks and 31 strikeouts in 35 innings.
Since July 24, he's allowed nine hits and eight earned runs in five appearances covering 3.1 innings.
The Nationals acquired Papelbon from the Philadelphia Phillies in July 2015. His tenure with the team will be remembered best for a physical altercation he had with Bryce Harper in the dugout during the final week of the season.
Papelbon was in a contract year. Washington will pay the remainder of his $11 million salary for 2016.
The Nationals hold a comfortable lead in the National League East and are preparing to make a playoff run. Moving on now from a player who didn't want to be there is only going to help them finish the season strong.
Given his age and performance decline this season, Papelbon should consider himself lucky if he's able to find a team that gives him a shot to pitch again in 2016.