He was born on April 1, 1848 in Hudson, Ohio, United States, the son of Nathan Perkins and Elizabeth (Day) Seymour. He was a direct descendant of Richard Seymour (or Seamer) who came from England to Hartford, Connecticut, in 1639; on his mother's side he was the grandson of Thomas Day of Hartford, secretary of state in Connecticut for twenty-five years. His great uncle was Jeremiah Day, president of Yale College.
Thomas Seymour grew up in the college atmosphere of Western Reserve, where his father's home was on the New England Green which served Hudson and the College as a reminder of their origin. His father was a professor of Greek and Latin.