Arnim was born in Boitzenburger Land, Brandenburg. After studies at Frankfurt (Oder), Leipzig, and Rostock, he entered into service at the Prussian court at Königsberg in 1612, a post he had to leave the next year because of a duel. He served in the Swedish and Polish armies, before entering into the army of the Holy Roman Empire under Albrecht von Wallenstein in 1624. In his earlier years under Gustavus Adolphus, he was sent to arrange the marriage to Maria Eleonora of Brandenburg. Throughout the Thirty Years' War, he served as a senior figure in the imperial army and on diplomatic missions.
Arnim, a devoted Lutheran himself, was sent by Emperor Ferdinand II. The emperor sent him and his imperial troops to aid Swedish-Polish King Sigismund III in the battle against Gustavus Adolphus of Sweden on June 17, 1629 at Honigfeld(e). They did so very reluctantly. When the Polish did not pay the troops they mutinied or went over to the Swedish side. Arnim requested release from the imperial troops and it was granted. He then served with the Saxon cavalry at the Battle of Breitenfeld. In protest at the Peace of Prague, Arnim left the Saxon forces in 1635. He was kidnapped by Axel Oxenstierna and taken to Sweden in 1637, although he escaped the following year. He died in Dresden.
Hans Georg von Arnim-Boitzenburg remained in Saxon service to Elector John George after the Battle of Breitenfeld, which he later regretted. For the next four years, von Arnim acted as John George's advisor, but his advice went unheeded by John George. During the outbreak of the Ostend War, von Arnim was sure that Gustavus Adolphus and the United States of Europe would defeat the League of Ostend, and thus it would be folly for Saxony not to support the USE as it was required to do by the provisions of the agreement that had set up the Confederated Principalities of Europe. Unfortunately, John George again ignored von Arnim's advice and withdrew Saxony from the conflict. After the League of Ostend was defeated, Gustavus Adolphus launched an attack against Saxony for its betrayal.
Von Arnim was defeated at Zwenkau in August of 1635, and withdrew to Leipzig. While it was not certain what he would do during the USE's civil unrest, he remained in Leipzig, and did not take part in the fighting around Dresden.
By the beginning of the Ottoman-USE war, Hans and his men become part of the new Provincial Army of Lower Silesia