Bench coach Tim Bogar will take over as interim manager.
Washington cited personal reasons for leaving and said it has nothing to do with the team's performance.
“I have submitted my resignation from the job I love – managing the Rangers – to devote my full attention to addressing an off-the-field personal matter. As painful as it is, stepping away from baseball is what’s best for me, my family," Washington said in a statement.
Washington was hired as the Rangers' manager in November 2006 after serving as a coach with the Oakland Athletics for 11 years.
The Rangers won the American League pennant in back-to-back years under Washington, beginning in 2010, and earned a wild-card berth in 2012. The team won 91 games in 2013 but fell short of the playoffs.
Texas has a major league-worst 53-87 record in 2014.
From a statement by general manager Jon Daniels:
"While we are disappointed, we accept Ron's decision and are grateful for his many contributions to the Rangers organization over the last eight years. This has certainly been a difficult season for our major league club in terms of on-field performance, but we were looking forward to moving ahead with Ron as our manager in 2015."
Daniels also said that Washington's decision to step down is not drug-related, according to ESPN's Tim MacMahon. Washington previously tested positive for cocaine during the 2009 season.
GALLERY: WHEN MAJOR LEAGUE MANAGERS WERE PLAYERS
- Molly Geary