Noble was born in Preston, and qualified as a doctor in 1833. In 1834 he moved to Manchester and was a medical officer for the Manchester Union. He was active during the typhus outbreak in Manchester in 1847, when he oversaw treatment of victims in special hospitals.
Noble was known as a specialist in nervous diseases, and wrote several books and articles on the subject, and wrote on hypnotism and phrenology. He was president of the Manchester Medical Society in 1864 and also president of the Manchester Statistical Society.