Edward Wyllys Andrews was born on March 25, 1856, in Chicago, Illinois, a son of Edmund Andrews (1824–1904), a doctor and pioneer in surgery and medical education.

He graduated from Northwestern University as valedictorian of his class of 1881. In 1883, he graduated from Chicago Medical College, which later became Northwestern University Medical School, and in that same year became one of the founders of the Chicago South-Side Medico-Social Society. He was a founder and organizer of both the American College of Surgeons and the National Board of Medical Examiners. He became a Fellow of the American Surgical Association, the Society of Clinical Surgery, the Chicago Surgical Society, and various other surgical societies, for several of which he served as president. He spent his career at what became Northwestern University Hospital but also had appointments at Michael Reese, Hospital Mercy Hospital, Cook County Hospital and St. Luke's Hospital. Andrews was a prolific writer on surgical topics, a member of the Chicago Literary Club, and an avid Shakespeare scholar, as well as a student of botany and geology.

In 1890, he married Alice Scranton Davis (1870–1945). He died on January 21, 1927, in Chicago, Cook County, Illinois.