Digital competitiveness is gaining more and more attention as a source of competitive advantage at the business and national economies levels. Digital economy performance is a matter of national strategies for achieving economic growth and socioeconomic development. Widely accepted instruments for reporting progress in these areas have been recently developed, including the Digital Economy and Society Index (DESI index). The current study aims to use the DESI index and its five dimensions (namely Connectivity, Human Capital, Use of Internet Services, Integration of Digital Technology and Digital Public Services) not only as a tool for recognizing the current state, but also to forecast progress under the Greek economic environment. The Gompertz model was used as a methodological tool and it is valuable that a diffusion model has been implemented on a composite index related to countries’ digital competitiveness. Moreover, the results reveal the areas where convergencies and divergencies exist between Greece and the rest of the EU-28 member states, while forecast permits one to evaluate how current policies have a significant impact on digital competitiveness. Results indicate that Greece is facing significant challenges as a result of the low state of digitization, coming from both the demand side (businesses that consume internet services) and the offer side (institutional and governmental constraints). The proposed results could be used in order to readjust existing policies and to spot aspects where further improvement is needed to achieve high standards of digital competitiveness.