Zimmermann, who turns 28 early next season, had a league-leading 19 wins last year and improved his five-year major-league career record to 43-35. He's started all 113 of his major-league appearances.
He was eligible for arbitration.
The Nationals also avoided arbitration with relief pitcher Drew Storen, 26. He's been in the major leagues for four seasons, appearing in 232 games, all in relief. He is 17-10 with a 3.40 earned run average and 55 saves. Storen agreed to a one-year contract.
Desmond, whose contract is for two years, played in 158 games last season, batting .280 with 20 home runs and 80 runs batted in. He's been named the National League Silver Slugger at shortstop each of the last two seasons.
Ramos hit .272 with 16 home runs and 59 RBI in 78 games in 2013.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys