Former NatWest investor specialists David Bermingham, Gary Mulgrew and Giles Darby failed in their challenge to the legality of extradition orders made by a Bow Street district judge and confirmed by Home Secretary Charles Clarke.
The trio, all UK citizens, are accused of defrauding Greenwich NatWest, a subsidiary of British parent company NatWest, of some 7.3 million US dollars (£4.2 million).
The alleged offences came to light following the collapse of the US energy company Enron, and led to the US government issuing extradition requests in February 2004.
The long-awaited judgment marks the first test case on the Government's 2003 Extradition Act, and several other high-profile cases are awaiting the outcome.
Lawyers for Mr Bermingham, of Goring, Oxfordshire, Mr Mulgrew, of Sible Hedingham, Essex, and Mr Darby, of Lower South Wraxall, Wiltshire, fought extradition on two fronts.
Firstly, they claimed that the Serious Fraud Office, not the Americans, should investigate the case - and any trial should take place in the UK.
Secondly, they argued that the offences are not extradition offences and that forcing the bankers to stand trial in the US would be unjust and incompatible with European and UK human rights law.
But Lord Justice Laws and Mr Justice Ouseley dismissed both challenges.
Lord Justice Laws ruled the case of the Enron Three "has very substantial connections with the United States and is perfectly properly triable there".
He said the facts disclosed "a significant United States dimension to the whole case. There is a Cayman Islands dimension as well."
It would be "unduly simplistic to treat the case as a domestic English affair".
The judge added: "The fact that the defendants could be prosecuted here - and that there would be consequential advantages and disadvantages from the prosecution and defence perspectives - does not amount to an exceptional circumstance."
Mr Justice Ouseley agreed, and both judges also ruled that the trio's extradition would not be "disproportionate" when set against their rights to private and family life under the European Convention on Human Rights.
Today's ruling marks the first test case on the Government's 2003 Extradition Act.
The new laws were largely justified by the UK Government as a necessary response to the terrorist attacks of September 2001. Commentators have remarked on the irony that the first challenge involves the City and has nothing to do with terrorism.
A key change is that certain countries, including the US, no longer have to produce prime facie evidence - proof that there is a case to answer - in order to have a suspect extradited from the UK. By contrast, US citizens cannot yet be extradited to Britain in a similar way.
The Home Office points out that there are safeguards in place, and no-one can be extradited unless sufficient information to justify a person's arrest pending extradition is produced to a district judge.
After today's ruling, the Enron Three's solicitor, Mark Spragg, spoke of the far reaching consequences of the court's decision that the director of the SFO had not been unreasonable in deciding not to commence an investigation, and possible
prosecution, of the trio in the UK.
He said: "This judgment means that no UK person or body has to decide which country should prosecute an alleged offence involving more than one country.
"Whichever country gets there first will, whatever its motives, seize jurisdiction - however severe the effects on a defendant and his family.
"The USA justice system has a long and aggressive extra-territorial reach, and will increasingly apply for the extradition of UK citizens for allegedly criminal conduct committed against UK institutions.
"There appear to be no legal protections against this at all."