Background Chagas disease is currently prevalent in European countries hosting large communities from Latin America. Whether asymptomatic individuals at risk of Chagas disease living in Europe should be screened and treated accordingly is unclear. We performed an economic evaluation of systematic Chagas disease screening of the Latin American population attending primary care centres in Europe. Methods We constructed a decision tree model that compared the test option (screening of asymptomatic individuals, treatment, and follow-up of positive cases) with the no-test option (screening, treating, and follow-up of symptomatic individuals). The decision tree included a Markov model with five states, related to the chronic stage of the disease: indeterminate, cardiomyopathy, gastrointestinal, response to treatment, and death. The model started with a target population of 100 000 individuals, of which 4·2% (95% CI 2·2–6·8) were estimated to be infected by Trypanosoma cruzi. The primary outcome was the incremental cost-effectiveness ratio (ICER) between test and no-test options. Deterministic and probabilistic analyses (Monte Carlo simulations) were performed. Findings In the deterministic analysis, total costs referred to 100 000 individuals in the test and no-test option were €30 903 406 and €6 597 403 respectively, with a difference of €24 306 003. The respective number of quality-adjusted life-years (QALYs) gained in the test and no-test option were 61 820·82 and 57 354·42. The ICER was €5442. In the probabilistic analysis, total costs for the test and no-test option were €32 163 649 (95% CI 31 263 705–33 063 593) and €6 904 764 (6 703 258–7 106 270), respectively. The respective number of QALYs gained was 64 634·35 (95% CI 62 809·6–66 459·1) and 59 875·73 (58 191·18–61 560·28). The difference in QALYs gained between the test and no test options was 4758·62 (95% CI 4618·42–4898·82). The incremental cost-effectiveness ratio (ICER) was €6840·75 (95% CI 2545–2759) per QALY gained for a treatment efficacy of 20% and €4243 per QALY gained for treatment efficacy of 50%. Even with a reduction in Chagas disease prevalence to 0·05% and with large variations in all the parameters, the test option would still be more cost-effective than the no-test option (less than €30000 per QALY). Interpretation Screening for Chagas disease in asymptomatic Latin American adults living in Europe is a cost-effective strategy. Findings of our model provide an important element to support the implementation of T cruzi screening programmes at primary health centres in European countries hosting Latin American migrants. Funding European Commission 7th Framework Program.