He said a new era had started, and he was the leader of a new National Party.
"We are drawing a line under the events of the past few years."
Luxon referred to National's long-established rural power base, paying tribute to farmers.
He also thanked former leader Judith Collins for her leadership of the party in a "difficult time."
Collins was ousted last week after her dramatic demotion of another former leader Simon Bridges.
Luxon said Collins, Bridges and Todd Muller all had "very important" roles to play in the future of the party.
"They have a unique set of skills we need to tap into... we'll set the baggage aside."
Luxon also spoke about National's catastrophic 2020 general election result.
"If you are one of the 413,000 voters who moved away from us, my message to you is: from today, National is back.
"New Zealand is at a critical crossroads as we grapple with, and emerge from, a global pandemic."
He then presented an aspirational message: "We have a choice: a choice between our current road to mediocrity, or a pathway to a more confident, aspirational and prosperous future."
Luxon warned that inflation was soaring.
"We are paying more than ever before at the checkout and the petrol pump, and everyday Kiwis are struggling to get ahead."
Luxon was asked about his Christian faith, and he said he kept religion and politics separate.
"People shouldn't be electing an MP because of their faith."
Luxon again said he'd had many conversations in recent days with other National MPs.
"There have been no commitments made" around positions, he said.
Luxon said the skills he learned as a corporate leader could be applied to politics.
"My background is very simply about leading very large complex organisations.
"I'm just really proud to be doing it with Nicola," Luxon said when asked why the more senior politician, Willis, was not the leader.
Luxon said he liked solving problems, and getting results.
He referred to the housing crisis and said National wanted to ensure more houses were built in a sustainable way. And he said New Zealand's major current economic problem was the same thing the country had grappled with for 30 years.
"The biggest problem we have in New Zealand is...we don't have a productive enough economy," Luxon said.
He said better investment in education was needed.
"Either we want to be a higher wage economy or we don't."
Luxon was asked how he could defeat Prime Minister Jacinda Ardern.
"Jacinda Ardern is a fine communicator, but the reality is we need much more."
Luxon rejected claims former National Party leader and PM John Key had been advising current MPs on how to vote after last week's leadership spill.
He said Key was a friend but added: "I'm not John Key. I'm Christopher Luxon."
Luxon said he was confident National's infighting could be stopped.
"We can because we are unified."
The new leader said he didn't feel he had to look over his shoulder or worry about betrayal.
"It's actually a team sport. It's actually about public service."
Luxon said Māori had done well under National, citing treaty settlements and the growth of the Māori economy under previous National administrations.
"We believe in an inclusive country"
Luxon told Newstalk ZB's Heather Du Plessis-Allan he is excited, fired up and ready to go.
Luxon said he decided pretty much at the time Judith Collins left that he wanted the job as leader of the party.
The roles of his MPs will be announced in the coming days.
The new leader admitted he loved all sorts of music but confessed to being a fan of "American music" - country and western.
Luxon also confessed that he hadn't been to church in the last five years, adding he was a non-denominational Christian.
Economy, education and getting people from dependence to independence are three things the "new" National Party will focus on, he said.
"The opportunity in politics, you take them when they're there. What's really exciting is that today our caucus demonstrated through an uncontested transition to new leadership that they wanted to unify and put the problems of the last four years behind them."
Last four years "completely dysfunctional"
Speaking to RNZ's Checkpoint, Luxon said the last four years were "completely dysfunctional".
"We had real conversations which each other about 'well do you want to keep doing it the way we have been doing it for the last four years which is completely dysfunctional or do you actually want to turn the page," he told Checkpoint.
Luxon said National MPs decided to have a reset and "look forward" which resulted in his run for leadership being uncontested.
Elected unopposed
Luxon's election was confirmed at 3.30pm, shortly after Bridges confirmed that he had dropped out of the race.
"It is a tremendous privilege to lead our great party, and I thank my colleagues for the confidence they have placed in me," Luxon said.
He said Willis would "do an incredible job and we will be a formidable team".
"I came to politics because I know how to solve problems and get things done.
"I have built a career out of reversing the fortunes of underperforming companies and I'll bring that real-world experience to this role.
"We are the new National Party that New Zealand needs."
MPs went into the caucus meeting at 3pm and Luxon was certain to be elected uncontested after his only real rival, Simon Bridges, dropped out of the contest about an hour before the meeting was to start.
Bridges announced he was dropping out of the race on Twitter, and said he would support Luxon for the job.
It followed last-minute talks between Bridges and Luxon this morning - understood to be the first time they had spoken since the contest began.
Mark Mitchell, one of Bridges' supporters, has now also thrown his support behind Luxon.
It is not yet known what positions Bridges has secured, but it is likely he was offered the finance portfolio and the number 3 ranking.
Bridges still has a sizable chunk of supporters in caucus, and including him and some colleagues in the top slots will help with caucus unity - and lend Bridges' experience to Luxon.
Bridges waited until the last minute to fold to see if he could secure enough support – the vote was said to be fairly close on Monday morning, although Luxon was said to have the edge from an early stage.
Other MPs and senior figures in National had been urging the two to come to an agreement rather than take it a potentially divisive vote.
The leadership opened up after caucus passed a motion of no confidence in Collins last Thursday. That followed her attempt to demote Bridges over a comment he had made to fellow MP Jacqui Dean six years ago – for which he had already apologised.
Earlier in the day, MPs arriving said the most important thing was to have unity after the meeting.
MP Chris Penk said he believed National was in "a more healthy position now" than it had been last week, but "we can and we must" unite behind a new leader.
"I think the same lesson applies now as it has for a couple of years, which is if we talk about the things that matter to New Zealanders we'll be okay, but if we don't then we will be lost. So we have to get back to focusing on those things that matter."
Louise Upston said she was confident the party would be able to united. "I think it's pretty obvious why we need a united team."
