It follows John's surprise resignation last week. Social housing minister Paula Bennett has been named as deputy prime minister.
The appointments were confirmed after a meeting of the National Party's caucus.
Bill, currently finance minister and deputy prime minister, will be officially sworn in at Government House in Wellington later on Monday.
Key quitting 'changes NZ political game'
New Zealand profile
In a tweet, Bill said he was "excited and humbled" to be elected.
In his first speech following his election, he said he would lead a "strong team of MPs, full of ideas".
He described Bennett as "smart, accomplished and energetic".
National Party President Peter Goodfellow said Bill and Paula would be "outstanding leaders" who would "provide a good mixture of experience and fresh thinking".
"Under their leadership, New Zealanders will continue to benefit from the stable government they expect, along with a dedicated focus on delivering results for families and businesses," he said.
Bill joined parliament in 1990 and has held several ministerial posts in education, health and finance.
John Key said his job required great sacrifices "from those who are dearest to me"
John said last week his decision to stand down was for family reasons and "the hardest decision I've ever made".
He said he would not be seeking a fourth term in the 2017 election.
John tweeted soon after Monday's announcement: "Congratulations to my good friend @honbillenglish on becoming the new leader of the @nznationalparty and the next Prime Minister of NZ."