Coleman won 38% of his 50 matches in charge of Wales while he guided the nation to their first semi-final of a major worldwide tournament when they reached the last four of the 2016 UEFA European Championship.
However, Wales failed to book their place in the 2018 World Cup finals, finishing third in Group D behind Serbia and the Republic of Ireland.
The Wales boss had been in talks to remain with the national team and had widespread support among both players and fans. "Kit Symons has also resigned from his position as National Team Coach and the FAW would like to put on record its gratitude for his commitment to the Wales National Team".
FA Wales chief executive Jonathan Ford said: "We are extremely disappointed to see Chris' tenure come to an end".
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Sunderland are bottom of the table, just six months after their relegation from the Premier League and sacked Simon Grayson last month after just 18 games in charge.
Appointed as the late Gary Speed's successor in January 2012, Coleman will go down as the most successful manager in his country's history after leading Wales to the European Championship semi-finals past year. The Black Cats are now sitting at the bottom of the Championship table.
He added: "We wish Chris the very best of luck for the future as he returns to club management, a desire for which he has always been honest and open about".