BACKGROUND: Long-acting injectable cabotegravir pre-exposure prophylaxis (PrEP) is recommended by WHO as an additional option for HIV prevention in sub-Saharan Africa, but there is concern that its introduction could lead to an increase in integrase-inhibitor resistance undermining treatment programmes that rely on dolutegravir. We aimed to project the health benefits and risks of cabotegravir-PrEP introduction in settings in sub-Saharan Africa. METHODS: With HIV Synthesis, an individual-based HIV model, we simulated 1000 setting-scenarios reflecting both variability and uncertainty about HIV epidemics in sub-Saharan Africa and compared outcomes for each with and without cabotegravir-PrEP introduction. PrEP use is assumed to be risk-informed and to be used only in 3-month periods (the time step for the model) when having condomless sex. We consider three groups at risk of integrase-inhibitor resistance emergence: people who start cabotegravir-PrEP after (unknowingly) being infected with HIV, those who seroconvert while on PrEP, and those with HIV who have residual cabotegravir drugs concentrations during the early tail period after recently stopping PrEP. We projected the outcomes of policies of cabotegravir-PrEP introduction and of no introduction in 2022 across 50 years. In 50% of setting-scenarios we considered that more sensitive nucleic-acid-based HIV diagnostic testing (NAT), rather than regular antibody-based HIV rapid testing, might be used to reduce resistance risk. For cost-effectiveness analysis we assumed in our base case a cost of cabotegravir-PrEP drug to be similar to oral PrEP, resulting in a total annual cost of USD$144 per year ($114 per year and $264 per year considered in sensitivity analyses), a cost-effectiveness threshold of $500 per disability-adjusted life years averted, and a discount rate of 3% per year. FINDINGS: Reflecting our assumptions on the appeal of cabotegravir-PrEP, its introduction is predicted to lead to a substantial increase in PrEP use with approximately 2·6% of the adult population (and 46% of those with a current indication for PrEP) receiving PrEP compared with 1·5% (28%) without cabotegravir-PrEP introduction across 20 years. As a result, HIV incidence is expected to be lower by 29% (90% range across setting-scenarios 6-52%) across the same period compared with no introduction of cabotegravir-PrEP. In people initiating antiretroviral therapy, the proportion with integrase-inhibitor resistance after 20 years is projected to be 1·7% (0-6·4%) without cabotegravir-PrEP introduction but 13·1% (4·1-30·9%) with. Cabotegravir-PrEP introduction is predicted to lower the proportion of all people on antiretroviral therapy with viral loads less than 1000 copies per mL by 0·9% (-2·5% to 0·3%) at 20 years. For an adult population of 10 million an overall decrease in number of AIDS deaths of about 4540 per year (-13 000 to -300) across 50 years is predicted, with little discernible benefit with NAT when compared with standard antibody-based rapid testing. AIDS deaths are predicted to be averted with cabotegravir-PrEP introduction in 99% of setting-scenarios. Across the 50-year time horizon, overall HIV programme costs are predicted to be similar regardless of whether cabotegravir-PrEP is introduced (total mean discounted annual HIV programme costs per year across 50 years is $151·3 million vs $150·7 million), assuming the use of standard antibody testing. With antibody-based rapid HIV testing, the introduction of cabotegravir-PrEP is predicted to be cost-effective under an assumed threshold of $500 per disability-adjusted life year averted in 82% of setting-scenarios at the cost of $144 per year, in 52% at $264, and in 87% at $114. INTERPRETATION: Despite leading to increases in integrase-inhibitor drug resistance, cabotegravir-PrEP introduction is likely to reduce AIDS deaths in addition to HIV incidence. Long-acting cabotegravir-PrEP is predicted to be cost-effective if delivered at similar cost to oral PrEP with antibody-based rapid HIV testing. FUNDING: Bill & Melinda Gates Foundation, National Institute of Allergy and Infectious Diseases of the National Institutes of Health.