The prime minister said that, after Brexit, the government will boost investment in public services while continuing to reduce debt.
People should know that "their hard work has paid off" and "the end is in sight", she said.
Ms May insisted the Conservatives would not allow "a return to the uncontrolled borrowing of the past" but said secure public finances "are not the limit of our ambition".
The announcement marks a major shift in the Conservatives' approach after eight years of eye-watering spending cuts and tax rises.
It will raise hopes of a significant increase in public spending during next year's Spending Review, along with potential tax cuts.
In a lengthy passage of her speech marked "end of austerity", Ms May told the conference in Birmingham: "We are not just a party to clean up a mess, we are the party to steer a course to a better future.
"Sound finances are essential, but they are not the limit of our ambition.
"Because you made sacrifices, there are better days ahead.
"So, when we’ve secured a good Brexit deal for Britain, at the Spending Review next year we will set out our approach for the future."
She added: "Debt as a share of the economy will continue to go down, support for public services will go up.
"Because, a decade after the financial crash, people need to know that the austerity it led to is over and that their hard work has paid off."
Ms May warned "there must be no return to the uncontrolled borrowing of the past, no undoing all the progress of the last eight years" but added: "But the British people need to know that the end is in sight. And our message to them must be this: we get it."
She used the speech to announce two new policies that signal the end of era of austerity.
The prime minister said the government would scrap a legal cap that limits how much councils can borrow to build new homes - a move No 10 officials admitted would increase public sector debt.
Ms May said: The last time Britain was building enough homes – half a century ago – local councils made a big contribution.
"At last year’s conference I announced an additional £2 billion for affordable housing, but something is still holding many of them back.
"There is a government cap on how much they can borrow against their Housing Revenue Account assets to fund new developments. Solving the housing crisis is the biggest domestic policy challenge of our generation.
"It doesn’t make sense to stop councils from playing their part in solving it, so today I can announce that we are scrapping that cap.
The prime minister also announced a new cancer strategy that will focus on early detection in a bid to improve survival rates.
It will be funded through the £20bn a year NHS cash boost that ministers announced earlier in the year.
Ms May said: "Through our Cancer Strategy, we will increase the early detection rate from one-in-two today, to-three-in four by 2028.
"We will do it by lowering the age at which we screen for bowel cancer from 60 to 50, by investing in the very latest scanners, and by building more Rapid Diagnostic Centres – one stop-shops that help people get treatment quicker.
"This will be a step-change in how we diagnose cancer. It will mean that by 2028, 55,000 more people will be alive five years after their diagnosis compared to today."
Labour said there would be no end to austerity as long as the Conservatives remained in power.
Ian Lavery, chairman of the Labour Party, said: “While the country is crying out for real change, all Theresa May and her party offer are pinched ideas and tinkering around at the edges, relying on petty attacks to cover up their lack of vision.
“Austerity is not an economic necessity. It is a political choice made by the Conservatives to hack away at our public services and communities, leaving workers worse off while gifting huge tax cuts to big business. And as long as Britain has a Conservative Prime Minister, we'll never see an end to austerity."
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