Brian Howes and his wife, Kerry Anne, now face being sent to Arizona to face the charges after judges rejected their case yesterday.
The couple had argued that extradition would violate their human rights, but the UK’s highest court in London found that there was an “overwhelming public interest” in honouring the American request.
Mr Howes had previously stated that they would take the case to the European Court of Human Rights if they lost the latest appeal.
In yesterday’s ruling, Lord Hope said that the crimes the Howes are accused of were “very serious” while a guilty verdict would be “likely to attract very long sentences”.
Lord Hope added that the Howes, who have six children, may be able to serve part of any prison term in a UK jail, but there is “no certainty that permission would be given”.
The court was shown an affidavit by William Bryan III, an assistant district attorney in Arizona, who said it would be “impossible” to state with precision how long the case may take to reach trial.
Mr Bryan also said it was a “more realistic assessment” that the Howes would be detained in custody in a US jail before the trial rather than released on bail.
Last July, the Howes lost a bid at the Court of Criminal Appeal in Edinburgh to stop them being sent to Arizona, but the same court later gave them leave to go to the Supreme Court.
The Bo’ness couple, who are accused of exporting chemicals to illegal drug labs producing highly addictive crystal meth, were arrested in January 2007 by police on behalf of the US Drug Enforcement Agency.
Mr Howes, 48, has been on remand since last April and has been on a number of hunger strikes in protest over his court battles and said he had made at least three suicide attempts. In January, he told the Evening News that he had split with his 34-year-old wife after she was left unable to cope with his remand while facing her own extradition.
Lawyers for Mr Howes had also argued before the Supreme Court that the case could be prosecuted in the UK. But Lord Hope said: “The United States has a substantial interest in trying [the Howes] in its own courts and there are strong practical reasons for concluding that that country, where most of the witnesses reside and the degree of criminality involved is best assessed, is the proper place for them to be tried.”
US authorities want to try the couple on 82 charges in connection with the alleged supply of banned chemicals.
If convicted in the US, the couple face a maximum penalty of 20 years in jail.
US authorities allege they sold chemicals via the internet knowing that they would be used to make crystal meth. The Howes maintain they ran a legitimate chemical business.