Born in 1901, Priess volunteered for military service in the army of the German Empire in January 1919, which was transformed to the Reichsheer in the Weimar Republic. Due to the limitations imposed by the Treaty of Versailles, his regiment was disbanded. He then joined the paramilitary groupFreikorps and fought against the Estonian War of Independence. In 1920, he returned to the army and was discharged in June 1931. On 24 October 1944, Priess succeeded Georg Keppler as commander of I SS Panzer Corps. He led this formation, as part of the 6th Panzer Army, in the failed Ardennenoffensive, which was dubbed the Battle of Bulge. The objective of the offensive was to split the British and American line in half, so the Germans could then proceed to encircle and destroy four Allied armies, forcing the Western Allies to negotiate a peace treaty with the Axis Powers. Subordinated to I SS Panzer Corps was Kampfgruppe "Peiper", led by Joachim Peiper. Peiper's command was responsible for the Malmedy massacre, a war crime in which 84 American prisoners of war were murdered by their German captors near Malmedy, Belgium. After the Ardennes offensive, the 6th SS Panzer Army was transferred to Hungary, where it fought against the advancing Soviet Army. The I SS Panzer Corps arrived in Hungary in early February 1945. There, Priess committed his forces in Operation Southwind against the Gran Bridgehead, a strong position formed by the Soviets over the Danube near the town of Gran, destroying the bridgehead by the end of February. He then commanded I SS Panzer Corps in Operation Spring Awakening, the last major German offensive of World War II. The attack, centered in the Lake Balaton area, began on 6 March 1945 and ended with a German defeat on 16 March 1945.
In May 1945, Priess surrendered to the U.S. forces. He started working for the US Army Historical Division at the Camp King. From May–July 1946, he became one of 73 defendants at the Malmedy massacre trial held in the Dachau internment camp. Along with Sepp Dietrich, Joachim Peiper and others, Priess was charged with the murder of over 300 Allied POWs and 100 Belgian civilians between 16 December 1944 and 13 January 1945. On 16 July, Priess was sentenced to 20 years imprisonment. In October 1954, he was released prior to serving his full sentence from the Landsberg Prison. Priess died in 1985.