Mr Osborne cited "tentative signs of a balanced, broad based and sustainable recovery", but stressed it was still the "early stages" and "plenty of risks" remained.
Mr Osborne said that recent months - which have seen more upbeat reports on the economy - had "decisively ended" questions about his economic policy.
Labour has dismissed the comments.
The speech comes ahead of the Conservative Party conference later this month, and after a number of forecasts and surveys pointed to an acceleration in the UK's economic recovery.
Revised gross domestic product figures showed the UK economy grew by 0.7% in the second quarter of the year, with predictions it could reach 1% for the third quarter.
And last week the OECD economic agency sharply increased its growth forecast for the UK economy this year to 1.5% from an earlier estimate of 0.8%.
By Nick RobinsonPolitical editor
The Conservatives' fear is that in future voters may not accept that current policies need to be maintained
Economic arguments have just begun
Mr Osborne said: "The economic collapse was even worse than we thought. Repairing it will take even longer than we hoped.
"But we held our nerve when many told us to abandon our plan. And as a result, thanks to the efforts and sacrifices of the British people, Britain is turning a corner.
"Of course, many risks remain. These are still the early stages of recovery. But we mustn't go back to square one. We mustn't lose what the British people have achieved.
"This is a hard, difficult road we have been following. But it is the only way to deliver a sustained, lasting improvement in the living standards of the British people."
The government's "economic plan is the right response to Britain's macroeconomic imbalances and the evidence shows that it is working", he said, in his address to an audience of academics, think tanks and businesses.
Mr Osborne said that those who advocated an alternative economic path could not explain recent improvements in the economic data.
And "the last few months have decisively ended" the idea that the scale and pace of his measures were to blame for much slower than projected growth over recent years, he added.
"Those in favour of a Plan B have lost the argument," he said.
Heeding calls to abandon the government's economic plan in order to spend and borrow more would have undermined the recovery and "would be disastrous" now, Mr Osborne said.
He pledged to remain "vigilant" to threats from abroad - including growing instability in the Middle East pushing up the oil price and a fresh eurozone crisis - as well as at home.
John Cridland, director-general of business lobby group CBI, said the economy was gathering some momentum, business confidence was rising and he expected growth to continue into next year.
"We have always said that deficit reduction should be at the top of the government's 'to-do list', but it must be coupled with an unrelenting focus on growth-boosting measures like infrastructure projects," he said.
By Stephanie FlandersEconomics editor
And he dismissed claims he was encouraging "the wrong sort of growth" - led by debt-fuelled consumer spending - insisting the evidence suggested "tentative signs of a balanced, broad based and sustainable recovery".
He said there were many tough decisions still to be taken and that "the only sustainable path to prosperity is to reject the old quick fixes and stick to the course we have set".
Labour accused Mr Osborne of "extraordinary complacency".
Opposition leader Ed Miliband told the BBC that the chancellor was "saying to people that he has saved the British economy at a time when, for ordinary families, life is getting worse".
"If ever you wanted proof that the government is out of touch with most people, that it is on the side of the few, George Osborne has provided it today," he added.
The UK economy is "turning a corner", Chancellor George Osborne has said in a speech in London.