Elisha Foote was born in Lee, Massachusetts, to Isaac Foote and Eunice (Nash) Foote. He was the younger brother of US Senator Samuel A. Foote.

Elisha married Eunice Newton, a union that fostered intellectual exchange and possibly collaboration. His legal background and interest in statistics may have been supportive to Eunice's scientific research.

Elisha Foote conducted scientific investigations of his own, particularly regarding solar radiation. He also had some inventions to his name. He may have collaborated with Eunice on her investigations.

Elisha Foote served as president of the American Association for the Advancement of Science.

Elisha Foote died in 1883, five years before Eunice.