The GCDH was officially inaugurated in June 2011 as a cross-faculty institution of Göttingen University in order to coordinate, carry out, and further develop research, teaching, and infrastructure activities at the Göttingen Research Campus in the field of Digital Humanities (DH). DH was hereby defined as the area of research, teaching, and development concerned with the intersection of computing and the various disciplines of the Humanities. In the case of the GCDH, however, the area of interest was further extended to include more broadly the application of computing approaches to the Social Sciences, Economic Sciences, and Law, as well as research on the effects of the digitisation of society from the point of view of the aforementioned disciplines. This was due, in part, to the participation at the GCDH of the faculties of Social Science and the Business and Law Schools, in addition to the faculties of Philosophy (in a coordinating role) and Theology as well as the Göttingen State and University Library. The GCDH is also closely collaborating with other member institutions of the Göttingen Research Campus, such as the Göttingen Academy of Sciences and Humanities, the Herzog August Library in Wolfenbüttel, and the Max Planck Society and Max Planck Digital Library.

In September 2011, GCDH moved into its main offices in the historical Heyne House, where its organisational and coordinating centre now spreads over two floors. The Centre currently has over 30 constituent members, primarily professors. It employs almost 20 staff and project staff and has secured over €3.5 million in project funding. GCDH is governed by an Executive Board. Made up of many prominent personalities from the international DH community, an Advisory Board provides the centre with expert guidance in the area of DH.