BACKGROUND: In sub-Saharan Africa, health-care provision for chronic conditions is fragmented. The aim of this study was to determine whether integrated management of HIV, diabetes, and hypertension led to improved rates of retention in care for people with diabetes or hypertension without adversely affecting rates of HIV viral suppression among people with HIV when compared to standard vertical care in medium and large health facilities in Uganda and Tanzania. METHODS: In INTE-AFRICA, a pragmatic cluster-randomised, controlled trial, we randomly allocated primary health-care facilities in Uganda and Tanzania to provide either integrated care or standard care for HIV, diabetes, and hypertension. Random allocation (1:1) was stratified by location, infrastructure level, and by country, with a permuted block randomisation method. In the integrated care group, participants with HIV, diabetes, or hypertension were managed by the same health-care workers, used the same pharmacy, had similarly designed medical records, shared the same registration and waiting areas, and had an integrated laboratory service. In the standard care group, these services were delivered vertically for each condition. Patients were eligible to join the trial if they were living with confirmed HIV, diabetes, or hypertension, were aged 18 years or older, were living within the catchment population area of the health facility, and were likely to remain in the catchment population for 6 months. The coprimary outcomes, retention in care (attending a clinic within the last 6 months of study follow-up) for participants with either diabetes or hypertension (tested for superiority) and plasma viral load suppression for those with HIV (>1000 copies per mL; tested for non-inferiority, 10% margin), were analysed using generalised estimating equations in the intention-to-treat population. This trial is registered with ISCRTN 43896688. FINDINGS: Between June 30, 2020, and April 1, 2021 we randomly allocated 32 health facilities (17 in Uganda and 15 in Tanzania) with 7028 eligible participants to the integrated care or the standard care groups. Among participants with diabetes, hypertension, or both, 2298 (75·8%) of 3032 were female and 734 (24·2%) of 3032 were male. Of participants with HIV alone, 2365 (70·3%) of 3365 were female and 1000 (29·7%) of 3365 were male. Follow-up lasted for 12 months. Among participants with diabetes, hypertension, or both, the proportion alive and retained in care at study end was 1254 (89·0%) of 1409 in integrated care and 1457 (89·8%) of 1623 in standard care. The risk differences were -0·65% (95% CI -5·76 to 4·46; p=0·80) unadjusted and -0·60% (-5·46 to 4·26; p=0·81) adjusted. Among participants with HIV, the proportion who had a plasma viral load of less than 1000 copies per mL was 1412 (97·0%) of 1456 in integrated care and 1451 (97·3%) of 1491 in standard care. The differences were -0·37% (one-sided 95% CI -1·99 to 1·26; p<0·0001 unadjusted) and -0·36% (-1·99 to 1·28; p<0·0001 adjusted). INTERPRETATION: In sub-Saharan Africa, integrated chronic care services could achieve a high standard of care for people with diabetes or hypertension without adversely affecting outcomes for people with HIV. FUNDING: European Union Horizon 2020 and Global Alliance for Chronic Diseases.