Background: Although gay, bisexual, and other cisgender men who have sex with men (MSM) and transgender women have the highest HIV burden in Latin America, pre-exposure prophylaxis (PrEP) implementation is poor. We aimed to assess the feasibility of same-day oral PrEP delivery in Brazil, Mexico, and Peru. Methods: Implementation PrEP (ImPrEP) was a prospective, single-arm, open-label, multicentre PrEP implementation study conducted in Brazil (14 sites), Mexico (four sites), and Peru (ten sites). MSM and transgender women were eligible to participate if they were aged 18 years or older, HIV-negative, and reported one or more prespecified criteria. Enrolled participants received same-day initiation of daily oral PrEP (tenofovir disoproxil fumarate [300 mg] coformulated with emtricitabine [200 mg]). Follow-up visits were scheduled at week 4 and quarterly thereafter. We used logistic regression models to identify factors associated with early loss to follow-up (not returning after enrolment), PrEP adherence (medication possession ratio ≥0·6), and long-term PrEP engagement (attending three or more visits within 52 weeks). This study is registered at the Brazilian Registry of Clinical Trials, U1111-1217-6021. Findings: From Feb 6, 2018, to June 30, 2021, 9979 participants were screened and 9509 were enrolled (Brazil n=3928, Mexico n=3288, and Peru n=2293). 543 (5·7%) participants were transgender women, 8966 (94·3%) were cisgender men, and 2481 (26·1%) were aged 18-24 years. There were 12 185·25 person-years of follow-up. 795 (8·4%) of 9509 participants had early loss to follow-up, 6477 (68·1%) of 9509 were adherent to PrEP, and 5783 (70·3%) of 8225 had long-term PrEP engagement. Transgender women (adjusted odds ratio 1·60, 95% CI 1·20-2·14), participants aged 18-24 years (1·80, 1·49-2·18), and participants with primary education (2·18, 1·29-3·68) had increased odds of early loss to follow-up. Transgender women (0·56, 0·46-0·70), participants aged 18-24 years (0·52, 0·46-0·58), and those with primary education (0·60, 0·40-0·91) had lower odds of PrEP adherence. Transgender women (0·56, 0·45-0·71), participants aged 18-24 years (0·56, 0·49-0·64), and those with secondary education (0·74, 0·68-0·86) had lower odds of long-term PrEP engagement. HIV incidence was 0·85 per 100 person-years (95% CI 0·70-1·03) and was higher for transgender women, participants from Peru, those aged 18-24 years, Black and mixed-race participants, and participants who were non-adherent to PrEP. Interpretation: Same-day oral PrEP is feasible for MSM and transgender women in Latin America. Social and structural determinants of HIV vulnerability need to be addressed to fully achieve the benefits of PrEP.