Gary McKinnon was arrested in the UK in 2002 after US prosecutors charged him with illegally accessing computers, including the Pentagon, US army, navy and NASA systems, and causing $700,000 worth of damage.
Mr McKinnon claims he just wanted to find out whether aliens really existed and became obsessed with trawling large military networks for proof.
However, the House of Lords ruled the gravity of the charges should not be understated and they would carry a maximum life sentence under English law. It turned down his appeal against extradition.
Mr McKinnon's lawyers had argued that sending him to the US would breach his human rights, as he could be labelled an enemy combatant and sent to Guantanamo.
If found guilty in the US, Mr McKinnon could face up to 70 years in prison and fines of up to $1.75m (€1.12m).
Using his own computer at home in London, prosecutors say Mr McKinnon hacked into 97 computers belonging to and used by the US government between February 2001 and March 2002.
Gary McKinnon is accused of causing the entire US Army's Military District of Washington network of more than 2,000 computers to be shut down for 24 hours.
Using only a 56K dial-up modem and the hacking name 'Solo', he found many US security systems used an insecure Microsoft Windows programme with no password protection.
He then bought off-the-shelf software and scanned military networks, saying he found expert testimonies from senior figures reporting that technology obtained from extra-terrestrials did exist.
At the time of his indictment, US Attorney Paul McNulty said: 'Mr McKinnon is charged with the biggest military computer hack of all time.'
