The new banks will be standard retail operations concentrating on deposits and mortgages.
Mr Darling said this was the best way to ensure "proper competition and choice". He said having just "half a dozen big providers was not acceptable".
The new entrants would "have a clean sheet to come in and do things differently", he added.
The chancellor also said the government would be splitting up Northern Rock into two parts by the end of the year, with a view to selling off one part within the next three to four years.
The government had already said it wants to sell off the part of Northern Rock that holds savers' money, carries out new lending and holds some existing mortgages.
He also said the government was keen to divest some of its holdings in RBS and Lloyds.
The government currently holds a 70% stake in RBS and a 43% stake in Lloyds after last October's bail-outs.
BBC business correspondent Joe Lynam says the latest move represents "a gilt-edged opportunity for non-UK retail banks, especially from the US, to get a firm foothold in the highly profitable British banking market for as low a price as could be imagined a few years ago".
The Conservatives said the break up of the state-owned banks had already been "well trailed".
A spokesman added: "We have called for more competition in banking, and for government stakes to be used to strategic effect to that end."
The Lib Dems Treasury spokesman Vince Cable welcomed more competition in the banking sector but said there should be no urgency to the sales.
"We need to be careful that when these split-ups occur, the prime cuts are not offered to private investors and the scraps left to taxpayers," he said.
There were also concerns expressed about the timing of the sell-off.
Treasury select committee chairman John McFall MP said the assets should not be sold off for less than their market value.
"It is important to ensure that we get taxpayer return for this bail-out. I'm relaxed about the timescale. I do not want to sell off [bank assets] at a cheap price, I don't want a fire sale," he told the BBC.
Peter McNamara, former head of personal banking at Lloyds TSB and managing director of the Alliance and Leicester, said that restructuring the banks in the current climate could in fact prove counter productive.
"Half the banks in the UK are suddenly going to be reorganised when you could argue their day job is to support industry and consumers during the recession. Without that support, we are more likely to have a steeper rise in unemployment," he said.
The government needs permission to break-up the banks from European competition commissioner Neelie Kroes.
Last week, the EU approved the plans for Northern Rock to be split in two.
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