Otto Henry was the eldest son of the Duke Otto II of Brunswick-Harburg (1528–1603) from his first marriage with Margaret (1530–1559), the daughter of the Count John Henry of Schwarzburg-Leutenberg.
He was taught science, but Otto II had strictly forbidden the instruction of fine arts.
Otto Henry studied at the University of Strasbourg, and was a canon at Bremen for a while, but then chose a military career.
In 1590, he led the cavalry of the Duke Alessandro Farnese in the Eighty Years' War and showed great courage in the battle of Ivry on 14 March 1590.
Otto Henry married in 1588 with Marie d'Henin-Lietard (d. 1606), the daughter of Count Jean de Bossu, with whom he had a son.