Born on November 20, 1919 in the Manhattan borough of New York City, Jane Cooke Wright was the oldest of two daughters born to Louis Tompkins and Corinne (née Cooke) Wright. Her mother was a professional educator and her father was among the first African-Americans to graduate from Harvard Medical School. He also was a graduate of Meharry Medical College of Nashville, which, founded in 1876, was the first medical school for African-Americans in the South.
Jane Cooke Wright was educated at the Ethical Culture School and the Fieldston School, from where she graduated in 1938. Upon completing her matriculation at Smith College in Northampton, Massachusetts, where she was a pre-med student, she accepted a full academic scholarship from New York Medical College in 1942. Only one of the college’s few African-American students, she was elected vice president of her class and president of the Honor Society. After graduating with honors in 1945, Wright accepted an internship at Bellevue Hospital, where she served nine months as an assistant resident in internal medicine.
In 1947, Wright began her residency at Harlem Hospital, where she acted as chief resident. While in residency as a visiting physician, she also worked as a physician within New York City Public Schools. That same year, Wright married David Dallas Jones, Jr., an attorney who graduated Harvard Law School, and they had two daughters, Alison and Jane. In 1948, Wright would complete her residency at Harlem Hospital and the following year, she left her position within the metropolitan educational district to join her father, who established the Cancer Research Foundation at Harlem Hospital.