It follows Mr. Key'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.
Mr. English, currently finance minister and deputy prime minister, will be officially sworn in at Government House in Wellington later on Monday
In his first speech following his election, he said he would lead a "strong team of MPs, full of ideas".
He described Ms. Bennett as "smart, accomplished and energetic".
National Party President Peter Goodfellow said Mr. English and Ms. Bennett 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.
Mr. English joined parliament in 1990 and has held several ministerial posts in education, health and finance. Mr. Key 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.