Sunderland have not won a home league game since they beat Watford 1-0 in the Premier League on December 17 past year and were relegated in May having collected only 24 points.
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 a year ago.
The new challenge facing Coleman will be to steer bottom-of-the-table Sunderland up the Championship and away from relegation danger, with his appointment expected to be confirmed by Sunday.
FAW chief executive Jonathan Ford said: "We are extremely disappointed to see Chris' tenure as Wales manager come to an end".
Grant Potter isn’t happy that Paul Heckingbottom appears to be Martin Bain’s first choice for manager
Ally McCoist has revealed that he would be interested in holding discussions over the vacant managerial position at Sunderland.
Disappointment followed as Wales failed to reach the 2018 World Cup finals in Russian Federation. Robbie Stockdale will remain in charge in a caretaker capacity for Saturday's home game against Millwall, with Coleman set to be in the dugout for the first time on Tuesday night, when Sunderland travel to Aston Villa.
Eighteen days after parting company with Simon Grayson, Press Association Sport understands the Black Cats have persuaded the man who guided Wales to the semi-finals of Euro 2016 to take up the reins at the Stadium of Light. However, he would face a hard job if he took the role.
Barnsley's Paul Heckingbottom had also been heavily linked with the Black Cats, where he was a trainee, although it emerged on Friday that he was not in consideration.
Coleman spent six months in Spain before returning to England with Coventry but left two years later before a short spell with Greek side AEL.