Sending Haroon Aswat - a British citizen of Gujarati origin - to the US could lead to a deterioration in his mental health, breaching his human rights, the European Court of Human Rights had ruled in April.
The UK had asked for the case to be reconsidered by the court's Grand Chamber but that was rejected. The latest decision is final, which means the accused cannot be extradited now.
Washington officials first requested Aswat's extradition eight years ago, but in 2008 he was transferred from prison to Broadmoor high-security psychiatric hospital in Berkshire after being diagnosed with paranoid schizophrenia.
In its ruling in April, the European court said his mental and physical health could significantly worsen in the "more hostile" environment of a US prison where he would have no support from family or friends.