The 47-year-old will return to domestic football having previously coached Fulham and Coventry City.
His appointment is something of a coup for Sunderland, who are bottom of the Championship and staring at the prospect of back-to-back relegations.
Coleman has held the post of Wales manager since January 2012, taking over following the death of Gary Speed.
The FAW have also confirmed Coleman's assistant Kit Symons' resignation.
"We are extremely disappointed to see Chris' tenure as Wales manager come to an end".
Ahead of Saturday's clash with Millwall, for which caretaker boss Robbie Stockdale will be in charge, Sunderland have not won a home league game since December previous year.
The Black Cats sacked Simon Grayson after a disastrous start to the Championship season
Coleman qualified the side for last summer's European Championships, Wales' first major tournament since 1958, before making it all the way to the semi-finals where they were defeated by eventual winners Portugal.
Former Fulham and Coventry City boss Coleman will team up with Wales internationals Jonny Williams, on loan from Crystal Palace, and right-back Adam Matthews at Sunderland - both of which have played under Coleman at worldwide level.
"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".
Coleman, speaking in September said: "Jonny finished training, in a auto, straight up to Sunderland, medical, agreed everything". During his last game in charge, against Panama on Tuesday, the Wales supporters repeatedly urged him to stay on.
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