The Mariners announced the deal Wednesday afternoon. It was earlier reported by the Washington Post and FOXSports.com.
"We set out this winter to add offense to our club. With the addition of Mike Morse, along with the other veteran players we have added, we believe this will help us be a more complete offensive team," general manager Jack Zduriencik said in the team's press release.
"We wanted to add additional right-handed power and Mike is a major step in that direction. We are looking forward to having him join our club and compete with the other members on our roster in spring training."
The deal brings Morse, 30, back to where he began his career. He made his major league debut in 2005 with the Mariners, who traded him to Washington in 2009 for outfielder Ryan Langerhans.
Morse hit .294 with 67 home runs and 208 RBIs during four seasons with the Nationals. His best season was 2011, when he hit .303 with 31 home runs, both career highs.
Jaso, acquired in a trade with the Rays last offseason, hit .276 with 10 home runs and 50 RBIs during his only season with the Mariners.
With Jaso gone, Jesus Montero is the only catcher on the Mariners' roster.
According to the Washington Post, the Nationals acquired pitcher A.J. Cole from Oakland.