Mr Taylor toppled the party's first female leader 34 votes to 17 in a Friday leadership ballot, ending her tenure after only nine months.
"We must look ahead and put the disagreements of the recent past behind us," Mr Taylor told reporters following the leadership spill.
"The choice is simple for the Liberal Party: change or die. I choose change."
Mr Taylor said home ownership would form the centrepiece of his leadership alongside a focus on growing the economy.
The Liberals' migration policy would restrict those who did not share Australian values from entering, he said.
Victorian senator Jane Hume was elected Mr Taylor's deputy, knocking off Ted O'Brien, who will now likely lose his shadow treasurer portfolio.
Ms Ley said she would spend the coming weeks in her regional NSW electorate of Farrer, before tendering her resignation from parliament.
A by-election will then be needed to choose a new MP for Farrer in what looms as a significant early test for Mr Taylor.
He will need to prove he can stave off challenges from independents and right-wing minor party One Nation, who are riding higher than the Liberals in the polls.
Ms Ley took a veiled jab at Mr Taylor's backers, who had white-anted her leadership for months.
"It is important that the new leader gets clear air, something that is not always afforded to leaders," she said.
Pressed on whether he had undermined his predecessor, Mr Taylor maintained he had supported Ms Ley's leadership.
Ms Ley said she wished her successor well.
The avid punk rock lover ended her press conference saying she would "continue to find wisdom in one of punk's defining themes: a fearless and honest belief in yourself".
Ms Ley, dressed in a suffragette white suit, entered and emerged from the meeting flanked by her moderate backers.
But her leadership had already been declared terminal after Mr Taylor and a slate of her shadow ministry, including some former supporters, resigned their posts.
She becomes the party's second shortest-serving leader, having spent three more weeks in the job than Alexander Downer.
While Ms Ley's supporters mostly avoided commenting as they left the opposition party room, some appeared visibly frustrated.
Mr Taylor's backers were all smiles as they departed the meeting.
Ms Ley is one of a handful of parliamentarians who still have access to a generous, since-scrapped parliamentary pension scheme.
Senator Hume emerged victorious from the four-horse deputy race, returning to shadow cabinet after being dumped by Ms Ley following May's election.
Mr Taylor is already facing criticism for deposing the first female leader, with groups such as the Women's Electoral Lobby and Chief Executive Women offering a scathing assessment of the Liberal Party's actions.
Labor released attack ads targeting Mr Taylor minutes after the party room concluded, previewing where it would focus its attention in the next two years: his economic credibility.
Mr Taylor was the shadow treasurer and Senator Hume the finance spokeswoman during the Liberals' disastrous election showing in 2025, when they ran a platform of higher taxes.
Mr Taylor said the Liberal Party would focus on lower taxes.
"We got some big calls wrong, especially on personal income tax, and it won't happen again," Mr Taylor said.
Treasurer Jim Chalmers wasted no time in tearing down his old sparring partner.
"Angus has zero credibility on the economy and neither does the bin fire that is the coalition," he said.
