Coleman will succeed Simon Grayson, who was sacked after 18 games in charge.
The 47-year-old had been Wales boss for nearly six years and last summer guided his country to the semi-finals of Euro 2016.
Sunderland prop up the Championship table after a nightmare start to the season and are in danger of suffering back-to-back relegations.
Coleman is expected to quit as Wales boss and fill the vacancy at the Stadium of Light by Sunday, according to reports.
Coleman's decision to leave worldwide football will come as a massive disappointment to the Wales players, who made their feelings known as to how desperate they were for him to continue in the job after his spectacular success.More news: Unemployment Down Slightly in ME in October
Kit Symons has also left his coaching post at Wales and the former Fulham manager could be heading to Wearside with Coleman, with the new management team set to be in charge for Tuesday night's trip to Aston Villa. However, he was unable to build on the momentum from their successful France 2016 campaign and qualify the team for next summer's 2018 FIFA World Cup Russia™.
Chief executive Martin Bain has held talks with potential candidates in recent days and the odds on Barnsley's Paul Heckingbottom returning to the club where he was a trainee have tumbled to evens with some bookmakers.
The Sunderland managerial race continues to rumble on at the moment with Ally McCoist the latest man to now confirm that he would be interested in the job. However, he would face a hard job if he took the role.
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. He also had short spells overseas with Real Sociedad and AEL Athens.