BBC News, UK
Giles Carlyle-Clarke, 48, could get a long prison sentence if he is found to have been involved in a £60m deal to import drugs into the US in the 1980s.
Mr Carlyle-Clarke's family has owned the Winterborne Clenston estate in Dorset since 1066.
The father-of-two denies all the allegations and has fought a legal battle against extradition for over eight years.
The European Court of Human Rights rejected his case two weeks ago and he had previously lost a legal challenge in the High Court.
Mr Carlyle-Clarke is due to be flown to America on Wednesday to face trial in Mobile, Alabama.
He was arrested in December 1997 when it was alleged he brought a ship loaded with four tonnes of cannabis into Alabama.
Mr Carlyle-Clarke's solicitor, Graham Compton, said he was "pretty depressed" by the final court decision against him.