Sakellariou entered the Hellenic Naval Academy in 1906 and served in the Royal Hellenic Navy in the Balkan Wars and until 1918, when he was discharged due to his royalist convictions during the National Schism. As with many other royalist officers, he rejoined the military in the 1920s. In March 1935, as Rear Admiral, he commanded the naval forces that were dispatched to subdue the naval units that took part in the Venizelist coup attempt. After the coup's suppression, he served as president of the court martial that tried the mutinous officers, and was promoted to Chief of the Fleet.
From this post he played a key role in the bloodless coup of Georgios Kondylis on 10 October 1935, which quickly abolished the Second Hellenic Republic and restored the monarchy. In 1937, Sakellariou was appointed as Chief of the Navy General Staff, and continued in this post during the Greco-Italian War. Following the suicide of Prime Minister Alexandros Koryzis on 18 April 1941, during the German invasion of Greece, King George II named Sakellariou as Minister for Naval Affairs and Deputy Prime Minister (with Emmanouil Tsouderos assuming office as Prime Minister on 20 April). In the face of the German advance and the heavy losses suffered by the surface vessels to the Luftwaffe, Sakellariou ordered the remaining ships to evacuate Greece towards British-held Egypt, where the Greek king and his government arrived later to form a government in exile, which was based in Cairo until Liberation in 1944. Sakellariou resigned his government posts on 2 May 1942 but remained at the head of the Greek Navy throughout the war.
After Liberation, in 1946 he successfully stood for election in Parliament in the Attica-Boeotia prefecture under the banner of his own Panhellenic National Party. On 29 July 1947, he was named Minister of Supply and Minister of Merchant Marine in the Konstantinos Tsaldaris cabinet. In the succeeding cabinet of Themistoklis Sofoulis, he was once again Minister for Naval Affairs (until 18 November 1948). Finally, in the 1951-1952 Nikolaos Plastiras cabinet, Sakellariou was appointed as Minister for National Defence, until his resignation on 31 March 1952.
He died in 1982.