The scientific work of Leonidas Zervas had a global resonance and his contribution was recognised by multiple awards throughout his life. In 1960 he received an honorary doctorate from the University of Basel on the occasion of the university's 500th anniversary, upon recommendation of Hans Erlenmeyer and Nobel laureate Tadeusz Reichstein. In 1969 he was bestowed honorary membership of the American Society of Biological Chemists. In 1976 he was conferred the  (1st class) by the Socialist Republic of Romania. In the same year Zervas was made Foreign Member of the USSR Academy of Sciences, an indication of the great respect for his work in the Eastern Block, too. The Max-Bergmann-Kreis company of German peptide chemists planned to present Zervas with the first Max Bergmann golden medal for peptide chemistry in 1980, but his sudden death necessitated a posthumous award ceremony.
In honour of Zervas, a commemorative bust has been unveiled in his birthtown Megalopolis in 1991 and the main conference hall of the National Hellenic Research Foundation is called the "Leonidas Zervas amphitheatre".
The European Peptide Society has established the Leonidas Zervas Award "in commemoration of his outstanding contributions to peptide science", awarded biennially since 1988. The award is given to the "scientist who has made the most outstanding contributions to the chemistry, biochemistry and/or biology of peptides in the five years preceding the date of selection".