Background: Post-exposure prophylaxis (PEP) offers protection from HIV after condomless sex, but is not widely available in a timely manner in east, central, southern, and west Africa. To inform the potential pilot implementation of such an approach, we modelled the effect and cost-effectiveness of making PEP consisting of tenofovir, lamivudine, and dolutegravir (TLD) freely and locally available in communities without prescription, with the aim of enabling PEP use within 24 h of condomless sex. Free community availability of TLD (referred to as community TLD) might also result in some use of TLD as pre-exposure prophylaxis (PrEP) and as antiretroviral therapy for people living with HIV. Methods: Using an existing individual-based model (HIV Synthesis), we explicitly modelled the potential positive and negative effects of community TLD. Through the sampling of parameter values we created 1000 setting-scenarios, reflecting the uncertainty in assumptions and a range of settings similar to those seen in east, central, southern, and west Africa (with a median HIV prevalence of 14·8% in women and 8·1% in men). For each setting scenario, we considered the effects of community TLD. TLD PEP was assumed to have at least 90% efficacy in preventing HIV infection after condomless sex with a person living with HIV. Findings: The modelled effects of community TLD availability based on an assumed high uptake of TLD resulted in a mean reduction in incidence of 31% (90% range over setting scenarios, 6% increase to 57% decrease) over 20 years, with an HIV incidence reduction over 50 years in 91% of the 1000 setting scenarios, deaths averted in 55% of scenarios, reduction in costs in 92% of scenarios, and disability-adjusted life-years averted in 64% of scenarios with community TLD. Community TLD was cost-effective in 90% of setting scenarios and cost-saving (with disability-adjusted life-years averted) in 58% of scenarios. When only examining setting scenarios in which there was lower uptake of community TLD, community TLD is cost-effective in 92% of setting scenarios. Interpretation: The introduction of community TLD, enabling greater PEP access, is a promising approach to consider further in pilot implementation projects. Funding: Bill & Melinda Gates Foundation to the HIV Modelling Consortium.