Noah was born in Wolverhampton in 1885, the son of John and Elizabeth Teague. In 1901 he was living with his widowed mother in Hall Street, Wednesfield, Wolverhampton, along with his brother Thomas E. and sister Ann M. Noah was a miner points boy. In 1906, Noah married Kate Foster in Wolverhampton, and by 1911 they had moved to Moorthorpe, South Elmsall, Yorkshire. Noah was now a coal miner hewer.
Noah enlisted in the 6th Battalion of the King’s Own Yorkshire Light Infantry (number 18251), but was killed in action near Ypres on 19 July 1915. He is remembered at the Ypres (Menin Gate) Memorial.