Shortstop Ian Desmond also agreed to a two-year deal with the Nationals before Friday's deadline for submitting arbitration figures. Other Nationals players agreeing to contracts included former closer Drew Storen, catcher Wilson Ramos and left-handers Ross Detwiler and Jerry Blevins.
The extension buys out the final two years of arbitration for Zimmermann, who will be eligible for free agency after the 2015 season. The Nationals had been talking with Zimmermann and his agents about a longer extension, but the sides were unable to reach agreement before Friday's deadline.
Zimmermann, 27, went 19-9 with a 3.25 ERA in 2013, and finished seventh in National League Cy Young Award balloting. He was one of 10 Nationals players who were eligible for arbitration entering this offseason. Pitcher Stephen Strasburg recently avoided arbitration by agreeing to a one-year, $3.975 million contract for 2014.
Desmond hit .280 with 20 homers and 80 RBIs in 2013, along with a career-best .971 fielding percentage. He was an NL All-Star in 2012, when he hit 25 homers and helped Washington win its division.
Ramos hit .272 with 16 homers in only 287 at-bats, missing time because of leg injuries.
Storen was 4-2 with three saves and a 4.52 ERA in 61 2/3 innings in 2013, when he also was sent to Triple-A Syracuse in July for a brief stint in the minors. He had 43 saves in 2011, missed the first part of 2012 because of right elbow surgery, then was switched to a setup role last season after Washington signed Rafael Soriano.
Detwiler was 2-7 with a 4.04 ERA in 2013, splitting time between the rotation and bullpen.
Washington got Blevins from the Oakland Athletics in a trade last month. He was 5-0 with a 3.15 ERA in a career-high 67 games in 2013.
The Associated Press contributed to this report.