Eduard Böhm was born in the Italian city of Ancona where his father served with a small representative detachment of the Austro-Hungarian army. His father, Georg Böhm (1813–1893), had as a sergeant won a battlefield commission for bravery after the battle of Novara in 1849, been promoted to the rank of major upon his retirement in 1877, and been elevated to hereditary nobility in September 1885. In June 1885 he had received permission to attach his wife's (Maria Josepha Ermolli) maiden name to his family name, and hence the family was known as "von Böhm-Ermolli".
Böhm-Ermolli was trained at the cadet academy in St. Pölten and the Theresian Military Academy in Wiener Neustadt and entered the service on 1 September 1875 as a lieutenant in the dragoons. He served in a variety of line and staff positions, steadily rose through the ranks, being promoted to General of the Cavalry on 1 May 1912 and appointed commanding general of the 1st Army Corps in Kraków.
At the start of World War I, Böhm-Ermolli was given command of the Austrian 2nd Army, which was intended for action on the Serbian front. After the Russian Empire mobilised, the 2nd Army was diverted to the Russian front, where it reinforced the armies of Austria's German ally.
He then settled in his home town of Troppau in Austrian Silesia, which became part of Czechoslovakia in 1919, and the government of Czechoslovakia paid him his pension and honored him as a General 1st Class in the reserve. In 1928 he became an "Army General" of Czechoslovakia, even though he never served in the Czechoslovak army.
When the Sudetenland, the predominantly German settled regions along the fringes of Czechoslovakia, was annexed to Nazi Germany in 1938, he became a German subject and received an honorary promotion to Generalfeldmarschall of the German army. In addition he was appointed honorary colonel-in-chief of Infantry Regiment 28 in his hometown of Troppau (Opava). When he died in December 1941, he was accorded a state funeral with full military honors in Vienna.