Julian Alexander was the son of Charlton Henry Alexander and Matilda Macmillan Alexander. He received his secondary education in Jackson, Mississippi and attended Millsaps College and Southwestern Presbyterian University. He received an AB degree from Princeton University in 1908, and an LL.B. from the University of Mississippi School of Law in 1910.
In 1913, Julian married Corabel Wharton Roberts, with whom he had three children.
- Assistant U.S. Attorney for the Southern District of Mississippi (1916-1919)
- U.S. Attorney for the Southern District of Mississippi (1919-1922)
- Circuit Court judge for the seventh District of Mississippi (1934-1939)
- Associate justice for the Mississippi Supreme Court (1941-1953)
- Alexander, Julian P. 1953. Mississippi Jury Instructions. St. Paul: West Publishing Company.
Alexander died from coronary thrombosis in New Orleans, Louisiana, on January 1, 1953, while attending the Sugar Bowl football game at Tulane Stadium. He was interred at Cedar Lawn Cemetery in Jackson, Mississippi.
Alexander’s portrait is part of the Mississippi Hall of Fame located in the Old Capitol Museum to honor his significant contributions to the state of Mississippi.