Leigh beat off competition from Toulouse Olympique, London Broncos, Bradford Bulls, Featherstone Rovers and York City Knights to fill the 12th slot left vacant following the rejection of Toronto's bid to re-join the competition last month.
Duffy told the PA news agency: "I've just stopped crying - I'm so happy for everyone who has put so much work into the criteria document.
"We are Super League ready - we've got a stadium which is hosting World Cup games, a chairman who is putting in the money, and we've been there and done it.
"I think it's exciting more than daunting. We are straight in with getting up to speed, and our goal is to give it a good go and make sure we stay in Super League."
Leigh were the unanimous choice of an independent seven-person panel led by Lord Caine, which met four times and had eight hours of discussions before the verdict was announced.
Lord Caine said: "Each of the six applicants was judged strictly but fairly against the agreed criteria. All were of high quality and I would like to pay tribute to the clubs for that."
Leigh have not played in Super League since they were relegated in 2017, but had won all four of their games in this year's curtailed Championship campaign.
Toulouse, the Championship leaders when the coronavirus pandemic forced the season's abandonment in March, had been bidding to join Catalans Dragons as a French club in the top flight.
Toulouse said in a brief statement: "We are obviously disappointed but we are already focused on the next Championship season, with the same goal."
London, who were relegated last year on points difference, and who had been linked with a possible ground-share at AFC Wimbledon if selected, tweeted: "Our plans don't change, we will push on for promotion via the Championship."
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