Sunderland were relegated from the Premier League last season and are now sit bottom of the Championship, having won only one of their 16 games so far this season.
Coleman, who succeeded Gary Speed as Wales manager in 2012, is the country's most successful coach, having led them to the semi-final stage of the Euros past year.
Previously he had taken charge at Fulham between 2003 and 2007 before stints at Real Sociedad and Coventry City. The 47-year-old is expected to be confirmed as Simon Grayson's successor over the weekend in what will be a major boost for Sunderland and a huge blow for the Football Association of Wales, which had hoped to persuade Coleman to sign a new contract.
Coleman began his managerial career at Fulham, spending four years in charge of the Whites before a poor run of form saw him axed by Mohamed Al Fayed.
Taking the Sunderland job will mean a return to club management for the first time in five years for Coleman.
"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".
The Wales boss had been in talks to remain with the national team and had widespread support among both players and fans. He is being linked with a move away from Wales after they failed to qualify for the World Cup in Russian Federation.
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.
Caretaker boss Robbie Stockdale will take charge of the Sunderland side for the visit of Millwall, with the Black Cats aiming to avoid holding the English record outright for the longest ever home winless streak. However, he would face a hard job if he took the role.