Zimmermann, 28, is a two-time All-Star and went 14-5 last season with a 2.66 ERA and 182 strikeouts. He tossed a no-hitter against the Miami Marlins in Washington's regular season finale.
Zimmermann is entering the final season of a two-year, $24 million contract after the two sides failed to agree to a long-term contract before last season. He has spent his entire career with the Nationals since being a second-round pick in 2007 and has a 57-40 career record with a 3.24 ERA.
Fister, 30, won 16 games with a 2.41 ERA for the Nationals last season, his first year with the team. Fister will make $7.2 million in 2015 and become a free agent following next season. He played for the Seattle Mariners and Detroit Tigers before joining the Nationals.
The Nationals finished 96-66 last season and won the NL East. They lost to the eventual World Series champion San Francisco Giants in the NLDS.
- Paul Palladino