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 a tweet, Mr English said he was "excited and humbled" to be elected.
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.
Picture from Radio New Zealand