GGNB is administered by the GGNB Managing Board, which includes the speakers of all doctoral programs and (if not already included among the speakers) one representative of each participating institution and a student representative. The board takes all pertinent decisions and elects a spokesperson for a (renewable) 5-year term. The GGNB Managing Board is assisted by the GGNB office as a central management and service unit, which provides administrative support to the doctoral programs in matters including the assessment of the eligibility of applicants for admission, monitoring training activities and scheduled thesis advisory committee meetings, administration of doctoral exams, and management of finances.

An international scientific advisory board evaluates the GGNB regularly. In addition, measures of quality assurance include student evaluation and feedback on all training activities and the monitoring of the students' performance (publications, grades etc.) of each program by the GGNB board. Each program prepares an annual report that forms the basis for the internal evaluation.

GGNB is part of the Georg-August University School of Science (GAUSS), the degree-awarding body for all doctoral students of the mathematics and natural science faculties. GAUSS defines the general regulations for all graduate schools and programs in mathematics and natural sciences, and formally approves all ordinary faculty members and each of the doctoral programs.