Welby, 56, who only became the Bishop of Durham a year ago, said the announcement by British Prime Minister David Cameron’s Downing Street office was “astonishing and exciting”.
He will replace Rowan Williams, who will retire in January after a decade spent battling divisions in the worldwide Anglican communion of around 80 million people.
The prime minister’s official Twitter feed said: “Downing Street is pleased to announce the appointment of Justin Welby as the 105th Archbishop of Canterbury.”
The appointment had been officially approved by Queen Elizabeth II, who is the Supreme Governor of the Church of England as well as the British head of state, Downing Street said in a statement.
Welby would be enthroned as archbishop in Canterbury Cathedral, in southeastern England, on March 21, 2013, the Archbishop of Canterbury’s official office said in a statement.
“To be nominated to this post is both astonishing and exciting,” he told a press conference.
“It is something I never expected, and the last few weeks have been a very strange experience, to put it mildly.
“It is exciting because we are at one of those rare points where the tide of events is turning, and the church nationally, including the Church of England has great opportunities to match its very great but often hidden strengths.”
The decision on a new archbishop was much later than expected and comes after months of tortuous negotiations by a committee that met in secret to find a replacement for Williams.
But Welby had been the leading contender and bookmakers even suspended betting on him earlier this week after a number of huge bets were placed on him to be the next archbishop.
He was educated at the exclusive Eton College – where premier Cameron, London mayor Boris Johnson and second-in-line to the throne Prince William also studied – and Cambridge University.