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Coleman’s move to the Stadium of Light was widely expected after he resigned from the Wales job earlier this week.
The former Fulham boss has agreed a two-and-half year contract with Sunderland.
The 47-year-old is the Black Cats’ ninth manager in the last six seasons and replaces Simon Grayson, who was sacked at the end of last month after less than half a season in charge.
“It’s an honour to be appointed the manager of Sunderland AFC and I’m over the moon that the club believes I am the right man,” Coleman said after taking training on Sunday.
“The club worked incredibly hard to make sure we were a good fit and to show me the potential that can be achieved here.
“I believe that every person at this football club, every player and every supporter has a part to play in getting us back to where we belong.”
Coleman arrives in the north-east after six years as Wales boss, during which time he managed his country into the top 10 of FIFA’s world rankings after an unexpected run to the Euro 2016 semi-finals.
Despite that success, Coleman was unable to lead Wales to next year’s World Cup after failing to secure a place in the play-offs and reports about his likely departure surfaced immediately after that disappointment.
With the Wales chapter of his career now over, Coleman has joined a Sunderland side at their lowest ebb for years.
A 2-2 draw against Millwall on Saturday gave them an unwanted English record of 20 consecutive home games without a win.
Sunderland, relegated from the Premier League under David Moyes’s management last season, are bottom of the Championship table.
They are four points from safety heading into Coleman’s first match in charge away to Aston Villa on Tuesday.
Sunderland chief executive Martin Bain, who led the search for Grayson’s successor, said: “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.”
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