Background: The long-term impact of universal home-based testing and treatment as part of universal testing and treatment (UTT) on HIV incidence is unknown. We made projections using a detailed individual-based model of the effect of the intervention delivered in the HPTN 071 (PopART) cluster-randomised trial. Methods: In this modelling study, we fitted an individual-based model to the HIV epidemic and HIV care cascade in 21 high prevalence communities in Zambia and South Africa that were part of the PopART cluster-randomised trial (intervention period Nov 1, 2013, to Dec 31, 2017). The model represents coverage of home-based testing and counselling by age and sex, delivered as part of the trial, antiretroviral therapy (ART) uptake, and any changes in national guidelines on ART eligibility. In PopART, communities were randomly assigned to one of three arms: arm A received the full PopART intervention for all individuals who tested positive for HIV, arm B received the intervention with ART provided in accordance with national guidelines, and arm C received standard of care. We fitted the model to trial data twice using Approximate Bayesian Computation, once before data unblinding and then again after data unblinding. We compared projections of intervention impact with observed effects, and for four different scenarios of UTT up to Jan 1, 2030 in the study communities. Findings: Compared with standard of care, a 51% (95% credible interval 40-60) reduction in HIV incidence is projected if the trial intervention (arms A and B combined) is continued from 2020 to 2030, over and above a declining trend in HIV incidence under standard of care. Interpretation: A widespread and continued commitment to UTT via home-based testing and counselling can have a substantial effect on HIV incidence in high prevalence communities. Funding: National Institute of Allergy and Infectious Diseases, US President's Emergency Plan for AIDS Relief, International Initiative for Impact Evaluation, Bill & Melinda Gates Foundation, National Institute on Drug Abuse, and National Institute of Mental Health.