Appointed last summer, Moyes failed to keep the Black Cats in the top flight, and will not remain in charge for the 2017/18 Championship campaign; he has stepped down without claiming compensation.
Sunderland finished the 2016/17 season in last place in the Premier League table, claiming just six wins from 38 games, and picking up only 24 points.
Chairman Ellis Short said on the decision: “I pursued the services of David Moyes for a considerable period prior to his appointment last summer, which makes the announcement of his departure difficult for everyone concerned.
“Having worked tirelessly throughout the campaign to avoid relegation from the Premier League, David has chosen to leave the club without compensation, which is testament to his character.
“In the days ahead we will take some time for reflection, and then focus on recruitment and pre-season as we prepare for our Championship campaign. We wish David well in the future.”
Moyes added: “I would like to thank Ellis Short and the Board for giving me the opportunity to manage Sunderland and the fans for always being so passionately supportive of their club.
“I wish the players and my successor well in their efforts towards promotion back to the Premier League”.