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.