Precision medicine is being enabled in high-income countries by the growing availability of health data, increasing knowledge of the genetic determinants of disease and variation in response to treatment (pharmacogenomics), and the decreasing costs of data generation, which promote routine application of genomic technologies in the health sector. However, there is uncertainty about the feasibility of applying precision medicine approaches in low- and middle-income countries, due to the lack of population-specific knowledge, skills, and resources. The Human Heredity and Health in Africa (H3Africa) initiative was established to drive new research into the genetic and environmental basis for human diseases of relevance to Africans as well as to build capacity for genomic research on the continent. Precision medicine requires this capacity, in addition to reference data on local populations, and skills to analyze and interpret genomic data from the bedside. The H3Africa consortium is collectively processing samples and data for over 70,000 participants across the continent, accompanied in most cases by rich clinical information on a variety of non-communicable and infectious diseases. These projects are increasingly providing novel insights into the genetic basis of diseases in indigenous populations, insights that have the potential to drive the development of new diagnostics and treatments. The consortium has also invested significant resources into establishing high-quality biorepositories in Africa, a bioinformatic network, and a strong training program that has developed skills in genomic data analysis and interpretation among bioinformaticians, wet-lab researchers, and health-care professionals. Here, we describe the current perspectives of the H3Africa consortium and how it can contribute to making precision medicine in Africa a reality.