Chancellor George Osborne has backed most of the recommendations in the Vickers' banking report, including protecting retail banking from riskier investment activities.
Mr Osborne also backed the suggestion from the Independent Commission on Banking, which said that banks should keep back a bigger cushion of assets.
The changes are designed to avoid a repeat of the 2008 banking crisis.
He also said state-owned RBS would reduce the size of its investment bank.
The reforms to the banking sector mean the deposits and overdrafts of ordinary consumers and small businesses will be handled only by ring-fenced parts of banks, which will not be allowed to embark on risky investment activities.
Mr Osborne said: "Our objective is clear. We want to separate high street banking from investment banking, to protect the British economy, protect British taxpayers and make sure that nothing is too big too fail.
"Second, we will make sure the banks have bigger cushions so they are better able to withstand losses."
The Shadow Chancellor, Ed Balls, broadly welcomed the moves: "We on this side of the House are determined our part in implementing these proposals, as far as possible, in a cross-party spirit. Taxpayers, customers and businesses, angry at banking recklessness which forced a multi-billion pounds bailout, will expect nothing else."
Mr Osborne said the changes would cost the industry £3.5bn to £8bn a year, but he said the costs would be "far outweighed" by the benefit to the economy of avoiding future financial crises.
He said these could reach £9.5bn a year on "modest" assumptions.
The Chancellor also announced a major strategy change at Royal Bank of Scotland (RBS), namely a big reduction in the size and scope of its investment bank.
A Treasury source told the BBC that the reconstruction of RBS's investment bank would leave it close to the kind of investment bank once owned by NatWest, one more focused on UK companies.
RBS bought NatWest a decade ago.
Mr Osborne told MPs in the House of Commons that he supported plans by RBS to shrink its investment bank into a business more focused on UK companies.
This is expected to involve a significant retreat from North America, where the bank acquired a big presence when Sir Fred Goodwin was chief executive.
However, BBC business editor Robert Peston said that the reforms implemented by the government are not 100% as originally billed.
In one key area the banking industry has succeeded in getting the Treasury to water down one of Vickers' recommendations, he said.
This is the proposal that the biggest UK banks should have enough capital, plus loans that could be converted into capital, to cope with losses equal to one-fifth of the size of their total balance sheet.
Robert Peston reported that HSBC had successfully argued that it would be disproportionately expensive for it to do this. In HSBC's case they are much bigger outside the UK than inside.
The Treasury is expected to soften the blow by requiring the big banks to raise capital to support only that part of their balance sheet that British tax payers would have to support in a crisis.
However, our correspondent said Sir John Vickers and his commissioners had been successful in achieving most of their aims, and the UK's financial system would be overhauled.
"Our banks will in the coming five years be forced to undergo significant financial, cultural and managerial reconstruction," he said.
Lydia Prieg, finance researcher at the New Economics Foundation, said the reforms would not protect the taxpayer from any future banking crisis.
"Even an outright separation between retail and investment banking, which is not what we are getting, would leave individual banks with asset ratios equal to approximately 100% of the UK's GDP, ie that are too big to fail.
"Critics will say these reforms already come at too high a price, but even the government's upper estimate £8bn is a drop in the ocean compared to the cost of another banking bailout and still means we subsidise banks by approximately £40bn a year [as a result of their too-big-to-fail status]."
John Longworth, director general of the British Chambers of Commerce (BCC), said the reforms in themselves would not help the wider problem of businesses gaining access to bank lending.
"Businesses still find it difficult to get access to capital, or capital on reasonable terms, in what is a highly risk-averse environment.
"This creates the danger of slowing the recovery and it is possible that Vickers' recommendations could add to this problem.
"Given the timescales for the implementation of credit easing, the time may now have come for the government to consider the introduction of an SME bank."