The Strasbourg court held there would be no violation of human rights for those facing life and solitary confinement in a “supermax” prison.
Judges said they would consider further the case of another suspect because of mental health issues.
Prime Minister David Cameron said he was “very pleased” with the news.
“It’s quite right that we have a proper legal process, although sometimes you can be frustrated by how long things take,” he added.
The court’s decision is one of its most important since 9/11 because it approves of human rights in US maximum security prisons, making it easier for the UK to send suspects to its closest ally.
There could still hypothetically be an appeal against the court’s ruling in its final Grand Chamber – but in practice, very few cases are re-examined in that final forum.
The men have three months to try to persuade the Grand Chamber to reopen the entire case and examine it. If the men fail to launch an appeal, they will be extradited to the United States.
The family of one of the men, Babar Ahmad, who has been held for a record of nearly eight years without trial, said he would fight on against extradition.
Last week, he appealed in a BBC interview to be charged and tried in the UK because his alleged crimes were committed here.
Home Secretary Theresa May said: “I welcome the decision of the European Court of Human Rights to allow the extradition of Abu Hamza and other terror suspects.
“In five of the six cases, the Court found that extradition would not breach their human rights and in the remaining case, it asked for further information before taking a final decision.
“I will work to ensure that the suspects are handed over to the US authorities as quickly as possible.”
The European Court said there would be no breach of human rights if the men were to be held in solitary confinement at ADX Florence, a Federal Supermax jail in Colorado, used for people convicted of terrorism offences.
ADX Supermax Florence, Colorado, is also known as the Alcatraz of the Rockies.
It is reportedly equipped with 1,400 remote-controlled steel doors, motion detectors, pressure pads and gun towers.
Solitary confinement is a regular way of life in supermax regimes, with prisoners locked up for at least 23 hours each day.
Supporters say supermaxes are the most appropriate way to house the worst of the worst in the prison population.
Critics say they are an affront to human rights and tantamount to torture.
Abu Hamza is unlikely to be held at that jail because of his disabilities. The court also held that the life sentences each man faces would not breach human rights.
But in one case, Haroon Aswat, judges said they could not yet give the go-ahead to extradition because they needed to see more submissions on his schizophrenia and how that would be treated were he sent to the US.
The court said that the range of activities and services at ADX Florence were better than many European prisons.
It said: “Having fully considered all the evidence from both parties, including specifically prepared statements by officials at ADX Florence as well as letters provided by the US Department of Justice, the court held that conditions at ADX would not amount to ill-treatment.
“As concerned ADX’s restrictive conditions and lack of human contact, the court found that, if the applicants were convicted as charged, the US authorities would be justified in considering them a significant security risk and in imposing strict limitations on their ability to communicate with the outside world.
“The court finds that there are adequate opportunities for interaction between inmates. While inmates are in their cells talking to other inmates is possible, admittedly only through the ventilation system.
“Save for cases involving the death penalty, it has even more rarely found that there would be a violation of Article 3 (that no-one shall be subjected to torture or to inhuman or degrading treatment or punishment) if an applicant were to be removed to a state which had a long history of respect of democracy, human rights and the rule of law.”
Abu Hamza is charged with offences relating to hostage taking in Yemen and an alleged plot to set-up a terrorism training camp in the United States. Haroon Aswat is also accused in connection to the training camp.
Babar Ahmad and Talha Ahsan are accused of supporting terrorism through a website operated in London.
The final two men allegedly played a part in organising the 1998 US Embassy bombings in East Africa.
In an unrelated case earlier this year, the European Court blocked the deportation from the UK of a different radical cleric, Abu Qatada, to Jordan, saying he faced an unfair trial.