The Sustainable Development Goals (SDG) have become the international framework for sustainability policy. Its legacy is linked with the Millennium Development Goals (MDG), established in 2000. In this paper a scientometric analysis was conducted to: (1) Present a new methodological approach to identify the research output related to both SDGs and MDGs (M&SDGs) from 2000 to 2017, with the aim of mapping the global research related to M&SDGs; (2) Describe the thematic specialization based on keyword co-occurrence analysis and citation bursts; and (3) Classify the scientific output into individual SDGs (based on an ad-hoc glossary) and assess SDGs interconnections. Publications conceptually related to M&SDGs (defined by the set of M&SDG core publications and a scientometric expansion based on direct citations) were identified in the in-house CWTS Web of Science database. A total of 25,299 publications were analyzed, of which 21,653 (85.59%) were authored by Higher Education Institutions (HEIs) or academic research centers (RCs). The findings reveal the increasing participation of these organizations in this research (660 institutions in 2000–2005 to 1,744 institutions involved in 2012–2017). Some institutions present both a high production and specialization on M&SDG topics (e.g., London School of Hygiene & Tropical Medicine and World Health Organization); and others with a very high specialization although lower production levels (e.g., Stockholm Environment Institute). Regarding the specific topics of research, health (especially in developing countries), women, and socio-economic issues are the most salient. Moreover, it has been observed an important interlinkage in the research outputs of some SDGs (e.g., SDG11 “Sustainable Cities and Communities” and SDG3 “Good Health and Well-Being”). This study provides first evidence of such interconnections, and the results of this study could be useful for policymakers in order to promote a more evidenced-based setting for their research agendas on SDGs.