Kelman was born in Brooklyn, New York to David and Eva Kelman. He grew up in Queens where he attended Forest Hills High School. After graduation, he attended Boston's Tufts University, where he earned a B.S. degree, then studied medicine at the University of Geneva where he obtained his M.D. degree. After interning at Kings County Hospital, he did his residency (1956–1960) at Wills Eye Hospital in Philadelphia, then worked as an ophthalmologist at the Manhattan Eye, Ear and Throat Hospital in New York.
One of the cataract surgery techniques that Kelman developed, phacoemulsification, has become today's standard. Inspired by his dentist's ultrasonic tools, in 1967 Kelman introduced the technique that uses ultrasonic waves to emulsify the nucleus of the eye's lens to remove the cataracts without a large incision. This new surgery removed the need for an extended hospital stay and made the surgery less painful. It has helped 100 million people nationwide. "Dr. Kelman, who received the National Medal of Technology from President George H. W. Bush in 1992, was inducted [in February 2004] into the National Inventors Hall of Fame in Akron, Ohio. Neurosurgeons have adopted the technique and used similar tools to remove tumors from the brain and spinal cord." (Boston Globe)
In 2004, Kelman died of lung cancer in Boca Raton, Florida. He was survived by his wife, Ann, as well as five children, Lesley Kelman Koeppel, Jennifer, Evan, Jason, and Seth Kelman. His eldest son, David Joseph Kelman, died in 2003.
- EricC Nagouey (5 June 2004). "Dr. Charles Kelman, 74; Made Cataract Removal Easier". The New York Times. Retrieved 18 November 2017.
- Albert Lasker Clinical Medical Research Award, 2004. Charles Kelman, For revolutionizing the surgical removal of cataracts, turning a 10-day hospital stay into an outpatient procedure, and dramatically reducing complications.
- Charles Kelman, MD, father of phaco, dies, Ophthalmology Times, Jun 9, 2004
-  The US patent, MATERIAL REMOVAL APPARATUS AND METHOD EMPLOYING HIGH FREQUENCY VIBRATIONS