Coleman took training at the Academy of Light this morning ahead of his first game in charge of the Black Cats, away to Aston Villa on Tuesday night.
The former Wales manager has signed a two-and-a-half-year deal and replaces Simon Grayson who was sacked on October 31, within minutes of the 3-3 draw with Bolton Wanderers.
Sunderland have conducted a lengthy and thorough recruitment process and Bain is delighted to have got his man.
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Bain told the club website: "The football club has conducted a thorough process over the last three weeks to identify the best manager for the job, before and after which Chris was the clear first choice.
"We are delighted that he and Kit Symons, his assistant manager, have joined us, and are now focused on working together to get the football club moving in the right direction."
Coleman arrives on Wearside on the back of six memorable years as Wales boss, during which time he managed his country into the top ten of FIFA’s world rankings and an incredible run to the semi-finals of Euro 2016.
He has previously managed Fulham and Coventry City in the Football League.
Kit Symons has joined him on Wearside as his assistant with talks ongoing regarding other backroom members of staff.