The park's name is taken from the celebrated Hamilton teacher, coach and trainer, Captain (Cap) John Richard Cornelius (1882-1964). Originally a military instructor and lecturer, he became a regular teacher after being wounded in the First World War.
During his many years at Hamilton Central Collegiate Institute, Capt. Cornelius encouraged many young students to strive for greatness. He taught them courage, confidence and respect, particularly in track, rifle, and also, suprisingly, music and drama. Five of the Captain's relay runners competed in the 1924 Olympics in Paris, and 4 in the 1928 Olympics in Amsterdam. He also helped form the Hamilton Olympic Club.
Landscaping of Captain Cornelius Park was completed in 1985.