Born in Quakenbrück, Engel studied art history, English and French from 1912 to 1914.
From 1935, he was employed in the municipal archive in Bielefeld and studied in Münster with half his time of service.
Engel was chairman of the Historical Association for the County of Ravensberg [de] from 1944 to 1968.
Since 1990, the association has awarded the Gustav Engel Prize annually in memory of his work.
His burial place is on the Sennefriedhof [de] in Bielefeld where he died at the age of 96.