Müller grew up in Sweden, where his father worked as a professor of agriculture. He joined the Imperial Navy in 1871 and served in many different positions, including commander of a gunboat in East Asia, then officer on the staff of Prince Heinrich of Prussia. He was Adjutant from 1904 to Kaiser Wilhelm II. He was named to the Prussian nobility in 1900. In 1906 he succeeded Gustav von Senden-Bibran as Chief of the German Imperial Naval Cabinet, serving until the end of the German Empire in 1918. As chief of the Naval Cabinet, he dealt not only with technical issues, but also with the Court and many politicians. By the start of the First World War he had become an ally of Chancellor Theobald von Bethmann-Hollweg in his attempts to control and moderate the Kaiser's actions. As one of the Kaiser's principal military decision makers in the run-up to the First World War, he was more of a pro-war opinion than not. During the October 1911Second Moroccan Crisis, he told the Kaiser that "there are worse things than war." He saw a coming racial war in which the German race must be upheld against the Slav and Roman races. He was serving in this position at the start of the First World War. On 30 August the Kaiser named his brother Grossadmiral Prince Heinrich of Prussia as commander of the Baltic Sea Squadron. Müller advised against this as the Prince had held the largely ceremonial post of Navy Inspector General and was not really qualified for the post. The Kaiser agreed but saw the Baltic theater as not critical and intended to give his brother a capable staff. Only a few days later, Müller objected the mining by Prince Heinrich’s forces on 5 August of an area of Danish territorial waters, thus threatening Danish neutrality. Finally, after it was reported that Heinrich had lost his nerve at the prospect of battle with the Russians, other arrangements were made on 9 October 1914 to keep him from commanding any important actions. Once war was declared with Great Britain and Ireland in the early days of August 1914, Müller agreed with the Kaiser in favoring only a limited guerrilla war against Britain, with no use of capital ships, in order to allow a negotiated peace once France and Russia had been defeated. As the war progressed and the Kaiser withdrew into a sheltered life at Imperial Headquarters in an atmosphere of "fear of the world and flight from reality", Müller worked with Generaloberst Moriz von Lyncker at great lengths to persuade the Kaiser to spend more time on the business of the government in Berlin. Lyncker and Müller had long realized Wilhelm II’s lack of effective leadership, but hoped to protect the institution of the monarchy from a revolution in Germany. Nor did they want reforms that would turn Germany into a constitutional monarchy because Germany's greatness rested on its semi-absolutist constitution and royal prerogative. For them the Kaiser had to fulfill his symbolic purpose through occasional appearances in public but not be trusted with real responsibility for decision-making. Finally, by October 1918, he had decided that the Kaiser should abdicate to save the monarchy. In January 1917 he acquiesced to the decision for the implementation of unrestricted U-boat warfare on the basis of Admiral Henning von Holtzendorff's memorandum during Pless Conference on 9 January 1917. In his memoirs, he dealt intensively with the personality of Wilhelm II.
The Kaiser and His Court: The Diaries Note Books and Letters of Admiral Georg Alexander Von Muller Chief of the Naval Cabinet 1914–1918; Harcourt Brace and World.