BACKGROUND: COBRA-BPS (Control of Blood Pressure and Risk Attenuation-Bangladesh, Pakistan, Sri Lanka), a multi-component hypertension management programme that is led by community health workers, has been shown to be efficacious at reducing systolic blood pressure in rural communities in Bangladesh, Pakistan, and Sri Lanka. In this study, we aimed to assess the budget required to scale up the programme and the incremental cost-effectiveness ratios. METHODS: In a cluster-randomised trial of COBRA-BPS, individuals aged 40 years or older with hypertension who lived in 30 rural communities in Bangladesh, Pakistan, and Sri Lanka were deemed eligible for inclusion. Costs were quantified prospectively at baseline and during 2 years of the trial. All costs, including labour, rental, materials and supplies, and contracted services were recorded, stratified by programme activity. Incremental costs of scaling up COBRA-BPS to all eligible adults in areas covered by community health workers were estimated from the health ministry (public payer) perspective. FINDINGS: Between April 1, 2016, and Feb 28, 2017, 11 510 individuals were screened and 2645 were enrolled and included in the study. Participants were examined between May 8, 2016, and March 31, 2019. The first-year per-participant costs for COBRA-BPS were US$10·65 for Bangladesh, $10·25 for Pakistan, and $6·42 for Sri Lanka. Per-capita costs were $0·63 for Bangladesh, $0·29 for Pakistan, and $1·03 for Sri Lanka. Incremental cost-effectiveness ratios were $3430 for Bangladesh, $2270 for Pakistan, and $4080 for Sri Lanka, per cardiovascular disability-adjusted life year averted, which showed COBRA-BPS to be cost-effective in all three countries relative to the WHO-CHOICE threshold of three times gross domestic product per capita in each country. Using this threshold, the cost-effectiveness acceptability curves predicted that the probability of COBRA-BPS being cost-effective is 79·3% in Bangladesh, 85·2% in Pakistan, and 99·8% in Sri Lanka. INTERPRETATION: The low cost of scale-up and the cost-effectiveness of COBRA-BPS suggest that this programme is a viable strategy for responding to the growing cardiovascular disease epidemic in rural communities in low-income and middle-income countries where community health workers are present, and that it should qualify as a priority intervention across rural settings in south Asia and in other countries with similar demographics and health systems to those examined in this study. FUNDING: The UK Department of Health and Social Care, the UK Department for International Development, the Global Challenges Research Fund, the UK Medical Research Council, Wellcome Trust.