Two other ministers announced that they would challenge English for the leadership in a vote by party lawmakers on December 12, but both withdrew after it became clear that English had sufficient support to win.
Mr English now has the support of 31 party MPs out of the 59-member cabinet, while there is yet to be any public declaration of support for rival Jonathan Coleman, the Health Minister.
The party is due to meet on Monday to vote on a new leader.
During his resignation speech, Key endorsed English as the next prime minister. He led the country for eight years and renewal in 2017 was believed to be healthy for his government.
"I won't be talking about being a prime minister until I am one", he told reporters.
Police Minister Judith Collins has withdrawn from the leadership race, and says she now supports Mr English. The other challenger said he'd yet to count the numbers and wasn't ready to concede.
"But everyone is also very cognisant that the government, and the direction of the government, is well supported by the public of New Zealand at this point", Mr Joyce said. Ms Collins has been a strong supporter of Mr Barclay as he faces a selection contest later this month. Both said they would back Mr English.
Adams has reportedly declared her support for Bennett as deputy.
"We will deal with any policy issues on Monday". Since 2006, he has held the position of deputy leader.
Bernie Monk, whose son Michael was killed in the Pike disaster, says Bill English now has the chance to make good on his predecessor's promise. Backbench MPs Nuk Korako, Todd Muller, Chris Bishop and Alfred Ngaro are being picked for promotion.
The Cabinet will need to be a mixture of experience and younger enthusiasm for voters to notice the changes.
Mr Joyce had been considered a potential threat to Mr English.
In other moves that will switch things up next year, Labour's David Shearer is quitting for a United Nations in South Sudan, meaning a looming by-election in Mount Albert.
Since the PM's resignation, some politicians have called for an earlier vote. A by-election would stretch Labour's thin financial and people resources greatly and it must be tempting for National to push Labour harder.