Abu Hamza due in US court following extradition
Radical Muslim cleric Abu Hamza and four other terror suspects are due to appear in court in the US later.
The five men left the UK on two flights, hours after the High Court rejected their final appeals.
Abu Hamza, Adel Abdul Bary and Khaled al-Fawwaz are due in federal court in New York while Babar Ahmad and Tahla Ahsan will face a judge in Connecticut.
Prime Minister David Cameron said he was "sick to the back teeth" of people like Abu Hamza.
Home Secretary Theresa May said she was looking to speed up the extradition process after the long legal battle.
On Friday judges ruled the five men had not shown "new and compelling" reasons to stay in the UK.
Their decision came after the European Court of Human Rights backed successive UK courts in ruling for the extraditions after a process lasting more than eight years.
The men were on two planes that left RAF Mildenhall in Suffolk.
Abu Hamza faces 11 charges in the US relating to hostage taking, conspiracy to establish a militant training camp and calling for holy war in Afghanistan.
He is set to go before a judge within 24 hours of landing and will appear in an open hearing following his arrival at an airport in New York state.
Abu Hamza is then expected to be held at the Metropolitan Correction Centre in Manhattan, in an area reserved for high-profile prisoners.
A pre-trial hearing is likely to take place within about three weeks. The actual trial, which is expected take place in public, could take between one and three years.
Mr Cameron said: "I'm absolutely delighted that Abu Hamza is now out of this country.
"Like the rest of the public I'm sick to the back teeth of people who come here, threaten our country, who stay at vast expense to the taxpayer and we can't get rid of them.
"I'm delighted on this occasion we've managed to send this person off to a country where he will face justice."
On Friday High Court judges Sir John Thomas and Mr Justice Ousley said in their ruling there was an "overwhelming public interest in the functioning of the extradition system" and that there was "no appeal from our decision".
David Fein, the US Attorney for Connecticut, confirmed the arrival of the flight carrying Mr Ahmad and Mr Ahsan.
He said Mr Ahmad and Mr Ahsan were indicted in 2004 and 2006 respectively with offences "stemming from their involvement in, and operation of" websites "that allegedly provided material support to the Chechen Muhjahideen, the Taliban, and associated terrorist groups".
They will appear before New Haven Federal Court in the state, where an internet service provider was said to have been used to host one of the sites.
Mr Fein added: "This has been a lengthy process, but the government's commitment to presenting this case to a jury during a fair and open trial has never wavered."
Campaigners for the two men had failed in a legal challenge to the UK's decision not to charge them with offences allegedly committed in this country.
The plane carrying Abu Hamza and the other two men landed in the US shortly after Mr Ahmad and Mr Ahsan's flight, the US Attorney's office in New York has confirmed.
Mr al-Fawwaz and Mr Bary are accused of being aides to Osama Bin Laden in London.
Home Secretary Theresa May told BBC Radio 4's Today programme she would be looking at lessons from the judiciary, other countries, and scrutinising the levels of appeal available in the UK to "make some changes" to the extradition process.
"It is frustrating, I think everybody is frustrated at how long it has taken to extradite these particular individuals."
But she also insisted the government had acted "as properly and quickly as we can at every stage... the point is there is a lengthy process. I think we do need to make some changes."
Solicitor Michael Caplan QC told the BBC News Channel the delay in the extradition of Abu Hamza was "unpalatable" but he said the European court has a huge backlog of cases which had delayed the case.
He added: "Whatever someone's background is there is the liberty of the individual and that has to be gone through completely... whoever they are."
Alun Jones QC, who represented Abu Hamza in the High Court on Friday, denied the cleric's attempt to halt the extradition on the ground he was unfit to plead was a "delaying tactic".
He told the BBC's Newsnight programme: "We had a consultant psychiatrist who gave his opinion to the Home Office... that there had been a deterioration in Abu Hamza's mental condition, attributable to sleep deprivation for eight years.
"He's been kept in conditions of utmost severity."