Born in Utica, New York, Wiles was a pupil of his father, Lemuel M. Wiles. He also studied with William Merritt Chase and Arthur Beckwith in New York, and at Academie Julien with Lefebvre and Carolus-Duran in Paris. He later became an important illustrator for periodicals such as Scribners, Harpers and The Century.
Like Chase, Wiles made teaching an important part of his artistic career. Along with summer classes he taught privately on Long Island and in New York City, Wiles gave instruction at several prestigious art schools, including Chase's New York School of Art and the New York School of Fine and Applied Arts. Chase so admired Irving Wiles that after his death, Wiles was entrusted to finish several portraits in Chase's studio.
Wiles exhibited internationally and was honored with many awards including medals at the World's Columbian Expo, Chicago (1893), the Pan American Expo, Buffalo (1901), the Pan Pacific International Expo, San Francisco (1915) along with numerous others. He was also a member of many of the most important fine art societies and organizations of his time.