Gary McKinnon had challenged a decision by Home Secretary John Reid to send him to the United States to face trial.
He has been indicted in New Jersey and northern Virginia, accused of illegally accessing and damaging U.S. government computer networks.
Prosecutors alleged that McKinnon, 39, illegally accessed 97 U.S. government computers between February 2001 and March 2002, causing $700,000 in damages. U.S. officials said in 2003 that no classified material had been obtained.
U.S. authorities called his attack the biggest successful hacking effort against American military computer networks.
Lawyers for McKinnon, who was first arrested in 2002 and then released, has fought extradition in the British court system since 2005, when the U.S. request was first made. It was not immediately clear why U.S. officials took so long to seek extradition.
McKinnon's lawyer, Karen Todner, confirmed in 2005 a published report that McKinnon was motivated by a desire to expose the ease with which a civilian could breach government computer systems and by a strong conviction that the U.S. government was concealing evidence of UFOs.
Janet Boston, acting for the U.S. government, told Bow Street Magistrates' Court that McKinnon installed unauthorized software on computers used by NASA, the Defense Department, the Army, Navy and Air Force that permitted him to "completely control the computers."
"On one instance, the U.S. Army's military district of Washington network became inoperable," she said.
Police arrested the former computer engineer, known online as "Solo," at his home in Wood Green, north London, in 2005 under an extradition warrant.
When the case was first revealed in late 2002, U.S. officials said McKinnon faced up to 10 years in prison plus fines of $250,000 on each of eight counts.
District Judge Christopher Pratt set several conditions for the $9,200 bail, including that McKinnon be barred from applying for any travel documents and from using any computer equipment that gives access to the Internet.
British prosecutors concluded that while Britain could have jurisdiction, it would be impractical to try the case in the U.K. They said that it arose from an American-led investigation of offenses committed in the United States and that the evidence and witnesses needed to prosecute were all in America.