Mr English already had enough caucus support, and now has no other competition for the role after Judith Collins and Jonathan Coleman conceded defeat.
He told Checkpoint with John Campbell he was "very happy to be the only candidate, but I'm not a prime minister".
'It's just an amazing opportunity' - Bill English duration 6′ :47″ from Checkpoint Add to playlist Download
Speaking to reporters soon after Dr Coleman conceded, he said the caucus still had to formally meet on Monday before his leadership would be confirmed, and the question of who would serve as Deputy Prime Minister would have to wait until then.
"I only get to be the leader of the National Party - and therefore the Prime Minister - when the National Party MPs confirm that.
"At the moment they are engaged in sorting out the leadership team, that still has some way to go, and the plan at the moment is that the confirmation of the leadership team will be on Monday, not today," Mr English said.
Mr English paid tribute to the other leadership challengers.
"I want to thank Jonathan Coleman and Judith Collins for helping the caucus with a constructive discussion about the transition from the John Key-led government.
"John was a strong and positive influence on the caucus and it's been great to have the opportunity to talk through how the National Party caucus wants to reset government."
Mr English said he would not be endorsing a candidate for Deputy Prime Minister at this point, and would not be drawn on the timing of next year's election.
Paula Bennett and Simon Bridges are running for deputy leader and many National MPs say they are still undecided as to who they will vote for.
This morning Mr English said he would give Steven Joyce the finance portfolio if he won the party's leadership.
Ms Collins, who withdrew from the race earlier this afternoon, also declared her support for Mr English.
Thirty National MPs have publicly stated their support for Mr English, which would be enough to secure him the role.
The new prime minister will be sworn in on Tuesday.