Cook was born in King's Lynn, the son of John Thomas Cook of Leicester. He was educated at Wyggeston Grammar School, Leicester, and read the Semitic Languages tripos at Gonville and Caius College, Cambridge, where he graduated with first-class honours in 1894 and won the Mason Hebrew Prize and Jeremie Septuagint Prize. Employed for several years on the editorial staff of Encyclopedia Biblica, in 1904 he was appointed a college lecturer (at Caius) in Hebrew, a position he maintained until his appointment as Regius Professor in 1932. He was also a university lecturer in comparative religion from 1912 to 1920.
Cook married Annette Bell, who predeceased him. He died in Cambridge on 26 September 1949.