Thomas Whipple Connally was born in Atlanta, Georgia, on July 30, 1881 to Dr. Elijah Lewis Connally and Mary Virginia Brown Connally. His siblings were Captain Joseph Brown Connally, Frances Connally Hentz, Sally Brown Connally Martin, Mary Temperance Connally Spalding, and Elizabeth Grisham Connally.

In 1898, Thomas W. Connally attended Emory College in Atlanta and became affiliated with the Gamma Chapter of Chi Phi Fraternity. He was elected permanent president of his class at Emory College and graduated in 1902. Chi Phi Fraternity honored Connally in 1903 by electing him to a national office. In 1904, he received a law degree from the University of Georgia in Athens, Georgia, where he was again chosen to be the permanent president of his class and was involved with the Eta Chapter of Chi Phi Fraternity. Throughout his lifetime, Connally remained devoted to Chi Phi. In addition to Emory University and University of Georgia, Connally attended Yale University in New Haven, Connecticut, where he was elected to Phi Beta Kappa.

Connally was also involved in the Granite Club of the First Methodist Church of Atlanta (formerly the University Club). This club was organized in April of 1909 by Dr. J. S. French, a pastor of the Methodist Church, and promoted social relationships, the development of moral character, and the cultivation of intellectual strength. The club had approximately a dozen members, and met once a month with one member acting as host and another member reading a paper on a subject selected by him at each meeting. The reading was followed by a general discussion. Connally served as secretary, treasurer, and scribe during his membership with the Granite Club.

In 1925, Connally married Dorothy Copeland and they had two children: Sally Patricia Connally, (b. 1926) and Thomas Whipple Connally, Jr., (b. 1927). In December 1927, at the age of 46, Connally died suddenly of pneumonia. In addition to the previously mentioned accomplishments, Connally served as the secrectary, treasurer, and attorney of the Connally Real Estate Company. He was a leading figure in real estate circles in Atlanta and served as president of the Atlanta Association of Builders and Managers. In addition, Connally was a member of the Atlanta Board of Public Welfare. Connally founded three trust associations for Chi Phi Fraternity: the Gamma Trust Association at Emory University, the Eta Trust Association at University of Georgia, and the Omega Trust Association at Georgia Institute of Technology. At the time of his death, Connally was a trustee of Emory University and a member of the executive committee of Emory University Alumni Counsel. He also served as the treasurer of the Emory College Alumni Association.