We analyzed Medical Subject Headings (MeSH) from 21.6 million research articles indexed by PubMed to map this vast space of entities and their relations, providing insights into the origins and future of biomedical convergence. Detailed analysis of MeSH co-occurrence networks identifies three robust knowledge clusters: the vast universe of microscopic biological entities and structures; systems, disease and diagnostics; and emergent biological and social phenomena underlying the complex problems driving the health, behavioral and brain science frontiers. These domains integrated from the 1990s onward by way of technological and informatic capabilities that introduced highly controllable, scalable and permutable research processes and invaluable imaging techniques for illuminating fundamental structure-function-behavior questions. Article-level analysis confirms a positive relationship between team size and topical diversity, and shows convergence to be increasing in prominence but with recent saturation. Together, our results invite additional policy support for cross-disciplinary team assembly to harness transdisciplinary convergence.