Corning hailed from a prominent Albany family. His great-grandfather, Erastus Corning, was an industrialist who founded the New York Central Railroad and served in Congress and as Albany's mayor from 1834 to 1837. Another great-grandfather, Amasa J. Parker, was a member of Congress and prominent judge. Corning's father, Edwin Corning, was Lieutenant Governor of New York from 1927 to 1928. His uncle, Parker Corning, served as a member of the United States House of Representatives. His brother, Edwin Corning Jr. served as a member of the New York State Assembly. Corning was educated at The Albany Academy, Groton School, and Yale University (class of 1932). The Corning family was involved in several Albany-area businesses, and Corning started an insurance agency after his college graduation. While he served as mayor, his agency did not do business with the city of Albany, but did do business with Albany County, which Corning argued presented no conflict of interest, since he was not a county official.