Background: Individuals who were formerly incarcerated have high tuberculosis incidence, but are generally not considered among the risk groups eligible for tuberculosis prevention. We investigated the potential health impact and cost-effectiveness of Mycobacterium tuberculosis infection screening and tuberculosis preventive treatment (TPT) for individuals who were formerly incarcerated in Brazil. Methods: Using published evidence for Brazil, we constructed a Markov state transition model estimating tuberculosis-related health outcomes and costs among individuals who were formerly incarcerated, by simulating transitions between health states over time. The analysis compared tuberculosis infection screening and TPT, to no screening, considering a combination of M tuberculosis infection tests and TPT regimens. We quantified health effects as reductions in tuberculosis cases, tuberculosis deaths, and disability-adjusted life-years (DALYs). We assessed costs from a tuberculosis programme perspective. We report intervention cost-effectiveness as the incremental costs per DALY averted, and tested how results changed across subgroups of the target population. Findings: Compared with no intervention, an intervention incorporating tuberculin skin testing and treatment with 3 months of isoniazid and rifapentine would avert 31 (95% uncertainty interval 14–56) lifetime tuberculosis cases and 4·1 (1·4–5·8) lifetime tuberculosis deaths per 1000 individuals, and cost US$242 per DALY averted. All test and regimen combinations were cost-effective compared with no screening. Younger age, longer incarceration, and more recent prison release were each associated with significantly greater health benefits and more favourable cost-effectiveness ratios, although the intervention was cost-effective for all subgroups examined. Interpretation: M tuberculosis infection screening and TPT for individuals who were formerly incarcerated appears cost-effective, and would provide valuable health gains. Funding: National Institutes of Health. Translation: For the Portuguese translation of the abstract see Supplementary Materials section.