Henne was born in the village of Weiler, near Wangen im Allgäu. His father was a saddlemaker, and in 1919 Henne was apprenticed as a motor vehicle mechanic. He began racing in 1923 at Mühldorf, finishing third on a Megola in his debut event. By 1925 he was competing at the Monza Grand Prix, his first major international meeting, where he placed sixth in the 350cc class.
After joining the BMW works team, Henne quickly became one of Germany's foremost motorcycle racers. He won the German national championship in the 500cc class in 1926, the 750cc class in 1927, and took victory at the Targa Florio in 1928. He also competed in the International Six Days Trial, forming part of the winning German team in 1933, 1934, and 1935.
His most enduring achievement was his motorcycle land speed record campaign. Starting on 9 September 1929 at 216.6 km/h (134.6 mph) aboard a supercharged 750cc BMW, Henne systematically raised the record year after year. Over the course of his campaign he set a total of 76 land speed world records. His final mark, established on 28 November 1937, was 279.5 km/h (173.7 mph) on a fully faired 500cc supercharged BMW. That record remained unbroken for 14 years — an almost unparalleled span of dominance in the discipline.
In 1934, Henne was recruited to the Mercedes-Benz Grand Prix team, competing in two events driving a Mercedes-Benz W25. At the 1934 Italian Grand Prix he retired on the third lap. At the 1934 Czech Grand Prix he fell ill during the race; Hanns Geier took over the car and brought it home sixth. It was at the Coppa Acerbo in August 1934 that Henne appeared in close proximity to the fatal accident involving Guy Moll, whose P3 lost control while passing Henne's Mercedes on a narrow straight.
He moved into sports car racing in subsequent years, winning the two-litre class at the 1936 Eifelrennen in the BMW 328's first competitive appearance — a significant milestone for what would become one of the most celebrated pre-war sports cars. He had hoped to compete for BMW at the 1937 24 Hours of Le Mans but was injured in that year's Eifelrennen and missed the race.
Henne had earned his pilot's licence in 1932, but when World War II came he was declared unfit for Luftwaffe service due to the skull fractures and concussions accumulated during his racing career. After the war he developed a contract workshop with Mercedes-Benz. In 1991, aged 87, he founded the Ernst-Jakob-Henne Foundation to assist innocent victims of misfortune. From 1996 until his death in 2005 he lived in retirement on the Canary Islands with his wife. He died at the age of 101.
Henne's record-breaking career on two wheels placed him in a small category of interwar athletes who combined technical partnership with a major factory — in his case BMW — with systematic, year-on-year improvement in outright speed. His 14-year tenure as the holder of the motorcycle land speed record is exceptional by any measure, and his role in the early competitive career of the BMW 328 adds a further dimension to a career that bridged the golden age of motorcycle racing and the Silver Arrows era of Grand Prix motor sport.