Born in Erlangen, Rehm spent a large part of his school time in Strasbourg and in 1919 he took his Abitur at the Maximiliansgymnasium München [de].
In 1923, he received his doctorate with a thesis on the literary Renaissance image of the 18th and 19th centuries, and since 1929 he had been a private lecturer in the history of modern German literature in Munich.
Due to blatantly expressed criticism of the National Socialist ideology and politics, planned appointments to Würzburg, Marburg/Lahn, Göttingen and Strasbourg failed.
However, the denazification process after 1945 proved difficult due to his party membership; he was only fully rehabilitated in 1950.
After a temporary professorship, Rehm was permanent professor of modern German literary history at the University of Gießen from 1940.