Elion was born in New York City on January 23, 1918, to parents Robert Elion, a Lithuanian Jewish immigrant and a dentist, and Bertha Cohen, a Polish immigrant.
Elion lindi në New York City më 23 janar të vitit 1918,me prindër Robert Elion, një emigrant lituanez dhe një dentist, dhe Bertha Cohen, një emigrante polake.