Angelis was born in 1912 and graduated Greek military school (Scholi Evelpidon). He saw action in World War II. Eventually he rose to the rank of Lieutenant General and took part in the April 21, 1967, coup d'etat of Colonel George Papadopoulos, replacing royalist Grigorios Spantidakis as chief of the General Army Staff. In that capacity, he issued the order to the 3rd Army Corps to impose the "Prometheus plan" for a military takeover of Greece.
Following the abolition of the monarchy by the junta in 1973, Angelis was named Vice President under Papadopoulos. On November 25 of that same year, after a coup by Dimitrios Ioannidis, Angelis was replaced.