The "biggest transfer of power to local government in living memory" will give councils in England the right to hold onto £26 billion which they raise annually from business rates, Chancellor George Osborne has announced.
Mr Osborne's "devolution revolution" was welcomed by council representatives, who said it should help boost investment in infrastructure and public services.
But there was concern from some businesses that the reform - which tears up the rating arrangements installed by Margaret Thatcher in 1990 - could result in bigger bills for companies.
And TUC general secretary Frances O'Grady warned that "regional inequalities will get wider", unless safeguards are introduced for councils in disadvantaged areas with low business growth.
Under the new system, rather than handing over business rates to Whitehall to be redistributed to town halls in grants, local authorities will be able from 2020 to keep 100% of the cash they raise from local companies. Meanwhile the uniform business rate which imposes a single rate on every council will be abolished.
Councils will be freed to cut rates to attract new investment and jobs to their high streets and business parks, and elected mayors in big cities like London, Manchester and Sheffield will be allowed to add a premium - expected to be capped at 2p on top of the multiplier which currently stands just under 50p - to pay for major infrastructure projects.
A complex system of tariffs and top-ups, designed to ensure that disadvantaged areas do not lose out, will be frozen in its current state, meaning that any gains from future growth will go direct to the councils involved.
Central government currently takes in around £11.5 billion in business rates and redistributes £9.4 billion in grants. But sources close to the Chancellor said that the change will not represent a loss to the Treasury, as it will be offset by the devolution of extra responsibilities to local authorities.
Mr Osborne told the Conservative Party conference in Manchester his reform will create new incentives for local authorities to compete for business investment, restoring powers to councils whose wings had been clipped by successive governments - including Tories - over a period of decades.
"Power to the people. Let the devolution revolution begin," declared the Chancellor, as he told applauding delegates: "It's time to face facts. The way this country is run is broken. People feel remote from decisions that affect them. Initiative is suffocated. Our cities held back. There's no incentive to promote local enterprise. It's time we fixed it."
Under the new plan "attract a business, and you attract more money; regenerate a high street, and you'll reap the benefits; grow your area, and you'll grow your revenue too", he said.
The move was welcomed by the Local Government Association, which has long campaigned for councils to be allowed to keep more of the money they collect. LGA chair Gary Porter said: "Councils and businesses both agree that business rates should be a local tax set by local areas. It is right that all of the money which a business pays is retained by local government and this will be a vital boost to investment in infrastructure and public services."
CBI director-general John Cridland said: "If this bold announcement on business rates is a way to cut them, then it will spur councils to take a pro-growth approach, and has the CBI's support."
But he warned it "must not be a way to increase rates without the consent of the local business community", while Institute of Directors director general Simon Walker said companies "will not stand for local politicians using it as an excuse to hike taxes".
Mr Osborne used his speech to claim Tories were now "the builders" with a plan for a prosperous future for workers, while Jeremy Corbyn's Labour were "wreckers" who had "completely abandoned" working people as they lurched "off to the fringes of the left".
But shadow chancellor John McDonnell accused him of not living in the "real world", after the Chancellor failed to mention last week's closure of the Redcar steelworks at the cost of 1,700 jobs.
"Angela Eagle and I are in Redcar today meeting people who will be looking at that speech and won't be fooled by Osborne's smoke and mirrors," said Mr McDonnell. "They want substantive answers in the here and now and sadly George Osborne failed to offer them any today."
Mr Osborne confirmed the establishment of a new National Infrastructure Commission chaired by former Labour cabinet minister Lord Adonis, to drive forward major projects like roads, railways, airports and power stations which require planning and construction over a period of decades.
And he said he would step up asset sales to fund £5 billion of investment, sweep away planning rules delaying home-building on brownfield sites and create British Wealth Funds to encourage local government pension funds to invest in infrastructure.
His announcement on business tax was hailed by Lord Heseltine - who spearheaded moves to revive the English regions with his 1980s drive to regenerate Liverpool - as an opportunity to revive "the dynamism that made this country what it was in the 18th and 19th centuries".