Henne was born in the village of Weiler, near Wangen im Allgäu. His father was a saddlemaker. In 1919 Henne was apprenticed to a become a motor vehicle mechanic. He started racing in 1923 in Mühldorf, finishing third on a Megola in his first race. In 1925 he competed in the Monza Grand Prix, his first major international event, where he placed sixth in the 350cc class.
Henne soon became one of the most successful German motorcycle racers. After joining the BMW works team, he became the 1926 German champion in the 500cc class, 1927 German champion in the 750cc class and the 1928 winner of the Targa Florio in Sicily.
Starting on 9 September 1929 at 216.6 km/h (134.6 mph) on a supercharged 750 cc BMW, Henne achieved a total of 76 land speed world records, increasing his speed annually from 1929 to 1937. His last motorcycle land speed record was set on 28 November 1937 with a speed of 279.5 km/h (173.7 mph) on a fully faired 500cc supercharged BMW. This record stood for 14 years.
Having earned his pilot's licence in 1932, Henne was conscripted by the Luftwaffe during World War II, but was declared unfit due to the skull fractures and concussions he had suffered during his racing career. After the war, he developed a contract workshop with Mercedes-Benz. In 1991 he founded the Ernst-Jakob-Henne Foundation to help innocent victims of misfortune.
From 1996 until his death in 2005 at the age of 101, Henne lived in retirement with his wife on the Canary Islands.