Bill English New Zealand's new Prime Minister
The new Deputy Prime Minister will be Paula Bennett, Xinhua news agency cited the party as saying.
English, who was elected by his parliamentary caucus exactly a week after Key announced his resignation, stressed the government under his leadership would follow the same policy settings laid down under Key's eight years as the country's leader.
English said Economic Development Minister Steven Joyce would replace him as Finance Minister, but he declined on Monday to outline any further changes in his cabinet, saying they would be announced before Christmas.
The 54-year-old English had been deputy to Key and Finance Minister since the National Party came to power in 2008.
He was a farmer in South Island and policy analyst at the New Zealand Treasury before being elected to parliament in 1990.
English will lead the government into the next general election, which must take place by September next year.
He became National Party leader in 2001 and led the party to its worst ever general election defeat in 2002.
English described himself as an "active Catholic and proud of it" and said his faith was important to him. "It doesn't define me, but it's an important influence."
He said that New Zealand would continue to build on its "critical" relationship with the US under President-elect Donald Trump.
"The fundamental relationship is in great shape and we'd like to use the opportunity of the relationship with the US to influence them on issues that matter to us," he said.
Both English and Bennett were elected unopposed after rival candidates withdrew their nominations.
In terms of personality and background, English is commonly perceived to be as different from Key as he could be.
Key will take up a seat on the government's back benches until he leaves parliament next year.