Home Secretary John Reid has welcomed the US Senate's support of a controversial extradition treaty with the UK.
The treaty awaits formal approval from George Bush
Under the treaty, three bankers, known as the Nat West Three, were flown to the US in July this year to face fraud charges linked to bankrupt Enron.
Critics branded it one-way, saying it made it easier to extradite people from the UK than the US.
But diplomatic pressure followed and US senators have now ratified the treaty.
The ex-NatWest bankers - David Bermingham, Gary Mulgrew and Giles Darby - were extradited under a fast track procedure that became law in Britain in 2002.
The government had argued that the arrangement meant both countries had to produce an equivalent level of legal evidence when seeking extradition from the other nation.
But the treaty came under fierce attack from opposition parties, including Lib Dem Nick Clegg who said Mr Blair had "short-changed" the UK by signing a "lopsided" extradition agreement.
The fact that US senators had not signed up to the treaty meant that reciprocal arrangements for the extradition of US nationals to the UK were not in place.
At the height of the controversy, peers called for extraditions to the US to be suspended, but MPs never had the opportunity to ratify the decision.
The treaty still needs to be formally approved by US president, George Bush.
Mr Reid said he was "delighted" that several months of discussions and Home Office Minister Patricia Scotland's visit to the US over the summer succeeded in getting Senate agreement.
"The treaty is an important measure in our fight against serious international crime," he said.
"Crime does not respect borders and in this modern age it is vital that law enforcement officers around the world have the tools available in order to help fight crime in the 21st Century."
The US Ambassador to Britain, Robert Tuttle, also welcomed the Senate's support and said it would improve the administration of justice.
Earlier this month, Jeremy Crook, of software firm Peregrine Systems, became the latest Briton to be extradited over fraud charges which he denies.