Zervas was born in 1902 in the rural town of Megalopolis in Arcadia, southern Greece. He was the first of 7 children of lawyer and parliamentarian Theodoros Zervas with Vasiliki Zerva (née Gyftaki). After finishing secondary education at the local Gymnasion of Kalamata in 1918, he went to study Chemistry at the University of Athens. Before finishing his studies there, he moved to Berlin in 1921 where he graduated with a degree in chemistry from the University of Berlin in 1924.
Under the supervision of Max Bergmann, he finished his doctoral thesis on the reactions of amino acids with aldehydes and was awarded his Dr. rer. nat. from the University of Berlin in 1926. He proceeded to work with Bergmann in the Kaiser Wilhelm Institute for Leather Research in Dresden, of which Bergmann was the founder and director. From 1926 to 1929 Zervas was a research associate and eventually rose to head of the organic chemistry division and vice-director of the institute (1929–1934). It was at this period that the two men developed the Bergmann-Zervas oligopeptide synthesis which brought them international fame within academic circles.
Zervas, by that point a close personal friend of Bergmann, decided to follow the latter to the US in 1934 after Bergmann emigrated from Nazi Germany in 1933 under pressure due to his Jewish origin. In New York, Zervas spent 3 years as lecturer and researcher at the Rockefeller Institute for Medical Research.
In 1930, he married Hildegard Lange, and they remained together until his death.