The three former NatWest employees claimed that the decision by the home secretary Charles Clarke to allow their extradition to the US contravened their human rights.
The trio, David Bermingham, Gary Mulgrew and Giles Darby, all 43, stand accused of conspiring with senior Enron executives to defraud a NatWest subsidiary company of $7.3 million (Â£4.2 million).
The case could cost the three men as much as Â£1.5 million, if they are forced to face trial in the US rather than the UK, and they could be imprisoned for up to 25 years.
The bankers, who have been battling against extradition since 2004, have stated that they intend to take their appeal to the House of Lords and, possibly, the European Court of Human Rights.
Lord Justice Laws and Mr Justice Ouseley ruled this week: "It would be unduly simplistic to treat the case as a domestic English affair."