The case centering on Mustafa Kamal Mustafa, also known as Abu Hamza al-Masri, considered Britain's most recognizable extremist, has been closely watched as a sign of Europe's view on tough U.S. prisons.
The court said Britain would not violate EU human rights rules by extraditing the suspects, who could face life sentences in a maximum-security prison.
Al-Masri and the other suspects had argued that in the U.S. they could face prison conditions and jail terms that would expose them to "torture or inhuman or degrading treatment or punishment" in breach of the European human rights code.
The European Court of Human Rights in Strasbourg, France, rejected those claims, saying in a ruling Tuesday that "detention conditions and length of sentences of five alleged terrorists would not amount to ill-treatment if they were extradited to the USA."
However, the court said the five "should not be extradited" until its judgment becomes final -- a move that could take months -- or until a possible appeals process ends.
It also put off ruling on the case of a sixth suspect, Haroon Rashid Aswat, as it awaits further information about his schizophrenia and the conditions of his detention at a British hospital.
U.K. Prime Minister David Cameron said he was "very pleased" with the news.
"It is quite right that we have proper legal processes, although sometimes one can get frustrated with how long they take," he said.
The U.S. is also pleased with the judgement, according to a statement posted on the U.S. Embassy in London's website.
"We look forward to the court's decision becoming final and to the extradition of these defendants to stand trial in the United States," the statement said.
British Home Secretary Theresa May said the U.K. will work to see that the suspects are handed over to U.S. authorities as quickly as possible.
Based on charges filed in the U.S., the suspects could get lifelong jail terms without parole in maximum security conditions, such as cells with concrete furniture, timed showers, tiny windows and no outside communications.
The various challenges against extradition rested on the suspects' likely detention in the ADX Florence "Supermax" prison in Colorado, where they would be held in solitary confinement. In their ruling Tuesday, the judges found that conditions at ADX would not amount to ill-treatment.
Al-Masri, 53, who is blind in one eye and wears a hook for a hand, is known for his fiery anti-Western and anti-Semitic outbursts. He claims he has lost his Egyptian nationality, but Britain considers him an Egyptian citizen. The court listed him as a British national.
Al-Masri has also been linked to the taking of 16 hostages in Yemen in 1998 and to preaching jihad -- holy war -- in Afghanistan. He is also accused of setting up a terrorist training camp in rural Oregon.
In separate cases, Syed Talha Ahsan has been charged with conspiring to support terrorists via the Internet and 36-year-old Babar Ahmad is accused of running websites to raise money, appeal for fighters and provide equipment -- like gas masks and night vision goggles -- for terrorists.
Ahmad's father, Ashfaq, said he and his family were "very disappointed" by the court's decision, calling it "a serious abuse of process."
Ahmad hasn't faced charges in Britain, but has been held without trial for 8 years in a U.K. prison. In an interview that took place after the BBC won a legal battle to speak with Ahmad, he insisted he did not condone terrorism and urged authorities to put him on trial in the U.K.
Faras Baloch, a legal adviser to Ahmad's family, said their "best chance" of fighting extradition now lies in getting a trial in Britain.
"We are going to press for him to be tried in the U.K.," Baloch said, adding that justice should not be outsourced to the U.S.
Ahmad's brother-in-law, Fahad Ansari, said the family hoped to appeal to the European Court's grand chamber. He questioned the alleged "torture" and "inhuman and degrading treatment" in Supermax prisons.
"It is completely inhumane and no country can justify sending one of its citizens to such a scenario," he said.
Two other cases were also considered by the European court, which decided extradition to the U.S. would not violate EU human rights laws.
Khalid al-Fawwaz, a Saudi citizen, and Adel Abdul Bary, who is Egyptian, are wanted over the 1998 bombings of two U.S. embassies in Kenya and Tanzania that killed 224 people. Al-Fawwaz, allegedly Usama bin Laden's representative in Britain, has been charged with more than 269 counts of counts of murder.