The European Court of Human Rights has dismissed an attempt by five terrorism suspects to block their extradition from Britain to the United States.
The court in Strasbourg held there would be no violation of human rights for those facing life and solitary confinement in prison.
Judges said they would consider further the case of another suspect because of mental health issues.
The 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 prison in Colorado, used for people convicted of terrorism offences.
The BBC says court's decision is one of its most important since 9/11 because it makes it easier for Britain to send suspects to its closest ally.
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.
Home Secretary Theresa May said she would work to ensure that the suspects were handed over to the US "as quickly as possible".