European judges today ruled the move would be a breach of his human rights.
Aswat is currently being held at Broadmoor high-security psychiatric hospital and is wanted by US prosecutors for allegedly plotting with Hamza to set up a terror camp in Bly, Oregon.
Hamza was deported from the UK last year after a long legal battle when the Strasbourg court rejected his appeal.
In light of the medical evidence before it, the court found that there was a real risk to Mr Aswat
But today the ECHR decided that extraditing Aswat to the US would violate the paranoid schizophrenic's human right to be free from ill-treatment on account of the severity of his mental illness.