Born in Agrinio, he graduated from the Scholi Evelpidon Officer Academy in 1878 as a Second Lieutenant of Artillery, later followed by a further year of studies in Belgium. Upon his return, as Captain, he was appointed adjutant to the 1884-1887 French military mission, which had been tasked with modernizing the Greek Army. He was a recognized expert in artillery, teaching at the Army Academy and inventing the Schneider-Dangli Gun in 1893. During the Greco-Turkish War of 1897 he served as chief of staff of I Brigade in the Epirus sector. As a Lieutenant Colonel, he was transferred to the General Staff Corps in 1904.
Promoted to Colonel in 1907, he participated in the latter stages of the Macedonian Struggle, supervising operations in the Salonica area, under the nom de guerre of Parmenion. Promoted to Major General in 1911, he was appointed head of the Army General Staff in August 1912, partly because of his abilities, but also as a balance to the more royalist and Germanophile staff officers like Ioannis Metaxas. During the First Balkan War, he served as chief of staff to Crown Prince Constantine's Army of Thessaly until November 1912, when he became a member of the Greek delegation in the London Peace Conference. In March 1913 he was promoted to Lieutenant General and placed in command of the Epirus Army Corps.
In late 1914 he left the army and went into politics, joining the Liberal Party of Eleftherios Venizelos in 1915 and elected as an MP for Epirus. He became Minister for War and supported Venizelos during his struggle against King Constantine in 1916, joining his Triumvirate, the "Provisional Government of National Defence". In 1917, when Greece joined the First World War, he was appointed nominal commander-in-chief of the Greek Army, a position he retained until the war's end, when he returned to his parliamentary office. In 1921, Danglis succeeded the self-exiled Venizelos as president of the Liberal Party.