Greene earned his bachelor of science in special education at the University of Alabama in 1975 and master's degrees in special education and school psychometry at UAB in 1977 and 1979. He went on to complete a Ph.D in counseling and human development at Atlanta University in 1987. He also has certifications in school psychology and educational leadership from UAB.
Greene started his carreer in January 1975 as a teacher's aide, bus driver and substitute at the Allan Cott School. He was hired as a special education teacher at Jonesview Elementary School in Talladega that fall. He came to the Fairfield school system in that capacity at Robinson Elementary School in 1977 and took over the role of school psychometrist and coordinator of the school's emotional conflict program in 1979. In 1987 he was promoted to assistant principal of Fairfield High School for one year before he was named head school psychologist for the system. In 1991 he added the role of administrative assistant to the superintendent to his duties. In that position he worked to restructure and initiate numerous programs, especially for special-needs students. In 1993 he was named director of psychological services and in 2002 he was promoted to assistant superintendent. He was named interim superintendent in 2005 and was hired as permanent superintendent with a three-year contract in June 2007.
Citing a need for a change of direction, the Fairfield City School Board voted not to renew Greene's contract in their January 2010 meeting, then voted to go ahead and terminate it the following month. He was succeeded by acting superintendent Frieda Bush, who was previously the system's director of human resources. In January 2011 he was approved as principal of Robinson Elementary.
- Norris, Toraine (February 23, 2010) "Fairfield school board fires superintendent Anthony Greene." Birmingham News
- Norris, Toraine (January 12, 2011) "Fairfield school board approves move of former superintendent to principal's job." Birmingham News