The 50-year-old has made a swift return to the dugout just a week after he was sacked by Aston Villa following five straight Premier League defeats, signing a two-and-a-half-year deal at Carrow Road.
Smith replaces Daniel Farke, who was also axed last weekend despite overseeing Norwich’s first win of the season.
That victory at Brentford left the Canaries still bottom of the table and five points from safety.
Smith, who successfully fought a relegation battle with Villa during the 2019-20 season and will be assisted by Craig Shakespeare, told the club’s website: “It has been a whirlwind seven days, but I’m really pleased to be back and working for Norwich City in the Premier League.
“Clearly, there has been some wonderful work that has gone into this football club over last four and a half years. It is now the job of myself and Craig to continue and improve on that work with the ultimate aim of surviving in the Premier League.
“Norwich City is a big club. I was brought up in an era when Norwich were competing in Europe – I remember those times well and whenever I’ve visited Carrow Road and Norwich you can really sense the connection between the fans, staff and players. Together, we all have to make Carrow Road a really tough place for visiting teams.
“From the age of 16 I’ve been working in football. I think in that time I’ve had four months out and didn’t enjoy it. It’s great to get straight back in with a club that are determined to be progressive.
“I’ve always worked to improve and develop players – with that obviously comes improved performances. I was really impressed with the idea, structure and vision that is already in place at the club.”
Sporting director Stuart Webber said Smith’s track record made him the right man for the job and revealed he had been a “long-term target”.
“I have admired his work for some time and he has been a long-term target in the event that we needed to appoint a new head coach,” said Webber.
“Dean has an outstanding track record and as soon as he made it clear that he was ready to go straight back into a managerial role we contacted him immediately.
“He shares the same values and vision as the club, has a proven track record of winning games in the Premier League as well as developing players and building a winning culture and mentality.”
Smith’s first game at the helm will be at home to Southampton on Saturday – the same opponents as his last match in charge of Villa.