The court ruled that the suspects would not get "ill treatment" in supermaximum security prisons if they are extradited to the United States and convicted in American courts, according to a statement from the European court.
The court still needs to make a decision on one other suspect connected to the case.
The ruling adds another chapter to the long-running legal battle that started when the six suspects were indicted by the United States between 1999 and 2006. The suspects were all arrested in the United Kingdom and have been fighting extradition to the United States for years.
Several of the suspects were alleged to have links to Osama bin Laden, the European Court of Human Rights said.
One of the suspects, Mustafa Kamal Mustafa, who also is known as Abu Hamza, is wanted by the United States on 11 charges, including conspiracy in connection with a 1998 kidnapping in Yemen and conspiring with others to establish an Islamic jihad training camp in rural Oregon in 1999.
Another of the suspects, Babar Ahmad, is accused of providing material support to terrorists, conspiracy and money laundering. If convicted, he could face a life prison sentence.
The indictment against Ahmad accuses him of conspiring to provide support to terrorists, including helping to ship gas masks to the Taliban and using U.S.-based websites to raise money for Chechen leader Shamil Basayev. Basayev claimed responsibility for the 2004 Beslan school massacre in Russia. He was killed two years later by Russian agents.
U.S. Justice Department spokesman Dean Boyd welcomed the court ruling.
"We look forward to the court's decision becoming final and to the extradition of these defendants to stand trial in the United States," he said.
The ruling will not be final for another three months, according to court documents. Any party can refer the case to the Grand Chamber of the European Court of Human Rights within that period and request a further examination by a five-judge panel. If the request is refused, the judgment then becomes final.
British Home Secretary Theresa May also applauded Tuesday's ruling.
"I welcome the decision of the European Court of Human Rights to allow the extradition of Abu Hamza and other terror suspects," May said.
"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. We will work to ensure that the suspects are handed over to the U.S. authorities as quickly as possible."
The court delayed its decision on the sixth suspect, Haroon Rashid Aswat, while further information is provided regarding mental health issues.
Ahmad's family said it was disappointed in the decision and called for him to face trial in the United Kingdom.
"Babar has already been imprisoned without a trial for almost eight years, something he described in his recent interview to BBC as 'the most unimaginable type of psychological torture,'" a family statement said.
"Babar is a British citizen accused of a crime said to have been committed in the U.K. and all the evidence against him was gathered in this country. Nevertheless, British justice appears to have been subcontracted to the U.S."
The other suspects were identified as Syed Tahla Ahsan, Adel Abdul Bary and Khaled Al-Fawwaz.
