The European Court of Human Rights decision will be seen as long overdue by many.
Abu Hamza is wanted in the United States on terrorism charges. He has already been convicted here and served many years in jail.
He is accused of involvement in an attempt to set up a terror training camp in Oregon.
If the court had ruled against his deportation it would have been effectively questioning the standards of the United States' prisons and legal system.
He and four others who will also be extradited can appeal to the European 'grand chamber', so it may be some time before he is put on a flight to America. But, that he will face trial there now seems inevitable.