Noble was educated at Fraserburgh Academy, Scotland followed by University of Aberdeen and then Street John"s College, Cambridge where he graduated with a double first in Classics and Oriental Language. He was made a fellow of Street John"s College, Cambridge.
Noble was a lecturer in Latin at Liverpool University from 1926-1930. He then became Professor of Latin Language and Literature at the University of Leeds from 1930 to 1938 and then Regius Professor of Humanity at the University of Aberdeen from 1938 to 1952. He served as Principal of King"s College London from 1952 to 1968.
He was joint editor of Kharosthi Inscriptions.
