Rishi Sunak axed the HS2 project from Birmingham to Manchester and promised to use the GBP36 billion of savings to fund hundreds of other transport schemes.
The prime minister told his party's conference, taking place in Manchester, the HS2 project's costs had "more than doubled".
He said: "I say to those who backed the project in the first place, the facts have changed.
"And the right thing to do when the facts change is to have the courage to change direction."
As part of a drive to create a new northern network, he pledged to invest in a raft of other transport schemes.
"I am ending this long-running saga. I am cancelling the rest of the HS2 project and in its place, we will reinvest every single penny, £36 billion, in hundreds of new transport projects in the North and the Midlands, across the country.
"This means £36 billion of investment in the projects that will make a real difference across our nation."
Sunak confirmed the scheme will run to Euston in central London, rather than terminating at Old Oak Common in the capital's western suburbs, but promised to get a grip on the costs of the project.
He said the new plan for Euston will save £6.5 billion compared with HS2's vision.
"The management of HS2 will no longer be responsible for the Euston site," Sunak said.
"There must be some accountability for the mistakes made, for the mismanagement of this project.
"We will instead create a new Euston development zone building thousands of new homes for the next generation of homeowners, new business opportunities and a station that delivers the capacity we need."
Confirmation of the decision to axe the northern leg of HS2 came despite pleas from Tory West Midland mayor Andy Street to back the scheme.
With Street watching on, the Prime Minister said: "We will complete the line from Birmingham to Euston and yes, HS2 trains will still run here to Manchester and journey times will be cut between Manchester, Birmingham, London by 30 minutes.
"And I say this to Andy Street, a man I have huge admiration and respect for, I know we have different views on HS2.
"But I also know we can work together to ensure a faster, stronger spine, quicker trains and more capacity between Birmingham and Manchester."
Sunak – who presented himself as a politician who would take long-term decisions to fundamentally change the country – also set out a plan to effectively ban smoking.
He proposed raising the smoking age one year, every year, meaning a 14-year-old today could never legally be sold cigarettes.
The prime minister's view is controversial within a party which has a tendency to reject measures which curtail individual freedom, and Sunak said there would be a free vote in the Commons with his MPs not whipped to back the plan.
But he said: "We have a chance to cut cancer deaths by a quarter, significantly ease those pressures, and protect our children, and we should take it."
After 13 years of Conservative rule, Sunak faces a tough task to turn around the opinion polls ahead of a general election expected next year.
The prime minister said there was an "undeniable sense that politics just doesn't work the way it should" with a "broken system" but insisted he was the man to offer change.
Sunak, who was introduced by wife Akshata Murty, told the conference in Manchester "change is difficult, particularly for those who disagree".
But he said: "Where a consensus is false, we will challenge it. Where a vested interest is placing itself above the needs of the people, we will stop it.
"And where common sense is under attack from an organised assault we will defend it."
