Born in Hamburg, Ostermann joined the military service of the Luftwaffe in 1937 and was trained as a pilot. After a brief period with "Zerstörergeschwader" 1 (ZG 1), a heavy fighter unit, he was transferred to "Jagdgeschwader" 54 (JG 54). He participated in the Battle of France and Britain before transferring east. He became the sixth fighter pilot in aviation history to achieve 100 aerial victories on the Eastern Front for which he was awarded Knight's Cross of the Iron Cross with Oak Leaves and Swords. He was killed in aerial combat with Soviet fighters southeast of Lake Ilmen on 9 August 1942.