He was born in Volos, Greece but the family moved to Athens where he was educated in the Classical Gymnasium.
He studied civil engineering for four years in the and then in the Technical University Munich, receiving his Engineering Diploma in 1936.
His first job was at the Gollnow company in Stettin, where he was involved among other things in high radio transmitter masts. He was imprisoned by the Nazis for some time but with the help of Admiral Canaris he escaped to Switzerland where he continued his studies in Eidgenössische Technische Hochschule Zurich. In 1943, he joined the research department of the Royal Aeronautical Society in England.
Starting from 1949 he was lecturer in aeronautical engineering at the Imperial College London of the University of London, where he assumed a chair in 1955.
In 1959, Argyris was appointed a professor at the Technical University of Stuttgart (today University of Stuttgart) and director of the Institute for Statics and Dynamics of Aerospace Structures. He created the Aeronautical and Astronautical Campus of the University of Stuttgart as focal point for applications of digital computers and electronics.
Argyris was involved in and developed to a large extent the Finite Element Method along with Ray William Clough and Olgierd Zienkiewicz after an early mathematical pre-working of Richard Courant.
Royal Society; Romanian Academy.