Morse, who will report to Triple-A Syracuse, played in 107 games for the Mariners during his career and has a .300 career batting average with three home runs and 33 RBIs.
Morse can play first base, third and the corner outfield positions.
Langerhans played for Syracuse all season and had a .279 batting average with nine homers and 40 RBIs.
The Nationals dealt Langerhans to the Mariners to provide him a chance to play in the big leagues.
"We also made the trade to reward Ryan for his loyalty to the organization," acting general manager Mike Rizzo said. "He had a big Major League opportunity, and I didn't want to stand in his way."
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.