Murphy set a major league record with homers in six straight postseason games and earned National League Championship Series MVP honors.
He hit .281 with 38 doubles, 14 homers and 73 RBIs in 499 regular-season at-bats.
The long-ball total represented a career high as Murphy placed more emphasis on pulling the ball at the request of Mets hitting coach Kevin Long.
Murphy also was the hardest to strike out among major league qualifiers, fanning only once every 14.2 plate appearances.
After David Wright, Murphy had been the second-longest-tenured Met. He was drafted by the organization in the 13th round in 2006 out of Jacksonville University and made his major league debut on Aug. 2, 2008.
Murphy declined the Mets' $15.8 million, one-year qualifying offer after the season.
The Nationals give up their first-round pick (No. 18 overall) in next year's draft by signing Murphy, and the Mets will gain a compensation pick between the first and second rounds.
ESPN.com Mets reporter Adam Rubin contributed to this report.