Delphine Gibson was born on 17 August 1903 in Ridgeway, South Carolina, USA, into a family of sharecroppers. She was the second of eight children born to parents Elmore and Annie Tucker. In 1925, when she was a young woman, she decided to move to High Point, North Carolina, where she rented a room on Loflin Street. It was around this time when she met her future husband, Taylor Gibson, and the couple were married on 27 January 1928. Their first child, Frank Eugene Gibson, was born two years later in 1930. During this time, she was employed by Fli-Back Co., and also worked as a domestic worker. In 1952, she moved with her family to Pennsylvania.

On 1 September 1980, her husband died at the age of 88, and she began to lose her vision due to glaucoma around the same time; by 1982, she was completely blind. In 1998, it was reported that she and her caregiver had been granted a handicapped parking space due to her blindness. In 2004, at the age of 100, she moved into the Huntingdon Nursing and Rehabilitation Center. She attributed her longevity to good food, her faith in God, and her church. At the time of her 110th birthday in 2013, she was confined to a wheelchair, but was said to be in good spirits, singing church hymns and making jokes.

Delphine Gibson died on 9 May 2018 in Huntingdon, Pennsylvania, at the age of 114 years, 265 days.