Hoadly was born in Hartford, Connecticut, on August 1, 1828, the eldest son of William Henry Hoadley and Harriet Louisa Hillyer. After attending the Hopkins Grammar School in Hartford, he graduated valedictorian at Trinity College in 1851. Having earned his Bachelor of Arts degree, Hoadly then worked in the offices of the superintendent of public instruction while pursuing postgraduate education. Hoadly subsequently earned a Master of Arts degree from Trinity in 1854 and became the college's librarian that same year. He independently studied law and was admitted to the bar in the winter of 1855, though he never practiced law. In April, he was appointed Connecticut State Librarian, succeeding James Hammond Trumbull.
