Birrer completed his medical degree and doctorate of philosophy in 1982 in the Medical Scientist Training Program at the Albert Einstein College of Medicine in New York. Following a medical internship and residency at Massachusetts General Hospital, Birrer entered the Medical Oncology Fellowship program at the National Cancer Institute in Bethesda, Maryland. After his fellowship, Birrer was appointed senior investigator (with tenure) and established the molecular mechanism section in the Division of Cancer Prevention and Control. His clinical interests include ovarian cancer, endometrial cancer and cervical cancer.

In 2008, Birrer was appointed professor of medicine at the Harvard School of Medicine and assumed the position of director for both Gynecologic Medical Oncology at Massachusetts General Hospital and the Gynecologic Oncology Research Program at the Dana Farber/Harvard Cancer Center.

In 2017, he accepted the position of director of the O’Neal Comprehensive Cancer Center at the University of Alabama at Birmingham, where he served as professor of medicine, pathology and OB-GYN. He served as chair and chair emeritus of the Department of Defense Ovarian Cancer Research Program, chair of the Committee for Experimental Medicine of the Gynecologic Oncology Group, chair of the Translational Science Working Group of the Gynecologic Cancer Intergroup, and a member of the Gynecologic Cancer Steering Committee.