Background: Rivaroxaban has been shown to be efficacious for treatment of venous thromboembolism in adults, and has a reduced risk of bleeding compared with standard anticoagulants. We aimed to develop paediatric rivaroxaban regimens for the treatment of venous thromboembolism in children and adolescents. Methods: In this phase 2 programme, we did three studies to evaluate rivaroxaban treatment in children younger than 6 months, aged 6 months to 5 years, and aged 6–17 years. Our studies used a multicentre, single-arm design at 54 sites in Australia, Europe, Israel, Japan, and north America. We included children with objectively confirmed venous thromboembolism previously treated with low-molecular weight heparin, fondaparinux, or a vitamin K antagonist for at least 2 months or, in children who had catheter-related venous thromboembolism for at least 6 weeks. We administered rivaroxaban orally in a bodyweight-adjusted 20 mg-equivalent dose, based on physiologically-based pharmacokinetic modelling predictions and EINSTEIN-Jr phase 1 data in young adults, in either a once-daily (tablets; for those aged 6–17 years), twice-daily (in suspension; for those aged 6 months to 11 years), or three times-daily (in suspension; for those younger than 6 months) dosing regimen for 30 days (or 7 days for those younger than 6 months). The primary aim was to define rivaroxaban treatment regimens that match the target adult exposure range. The principal safety outcome was major bleeding and clinically relevant non-major bleeding. Analyses were per-protocol. The predefined efficacy outcomes were symptomatic recurrent venous thromboembolism, asymptomatic deterioration on repeat imaging at the end of the study treatment period. These trials are registered at ClinicalTrials.gov, numbers NCT02564718, NCT02309411, and NCT02234843. Findings: Between Feb 11, 2013, and Dec 20, 2017, we enrolled 93 children (ten children younger than 6 months; 15 children aged 6 months to 1 year; 25 children aged 2–5 years; 32 children aged 6–11 years; and 11 children aged 12–17 years) into our study. 89 (96%) children completed study treatment (30 days of treatment, or 7 days in those younger than 6 months), and 93 (100%) children received at least one dose of study treatment and were evaluable for the primary endpoints. None of the children had a major bleed, and four (4%, 95% CI 1·2–10·6) of these children had a clinically relevant non-major bleed (three children aged 12–17 years with menorrhagia and one child aged 6–11 years with gingival bleeding). We found no symptomatic recurrent venous thromboembolism in any patients (0%, 0·0–3·9). 24 (32%) of 75 patients with repeat imaging had their thrombotic burden resolved, 43 (57%) patients improved, and eight (11%) patients were unchanged. No patient deteriorated. We confirmed therapeutic rivaroxaban exposures with once-daily dosing in children with bodyweights of at least 30 kg and with twice-daily dosing in children with bodyweights of at least 20 kg and less than 30 kg. Children with low bodyweights (<20 kg, particularly <12 kg) showed low exposures so, for future studies, rivaroxaban dosages were revised for these weight categories, to match the target adult exposure range. 61 (66%) of 93 children had adverse events during the study. Pyrexia was the most common adverse event (ten [11%] events), and anaemia and neutropenia or febrile neutropenia were the most frequent grade 3 or worse events (four [4%] events each). No children died or were discontinued from rivaroxaban because of adverse events. Interpretation: Treatment with bodyweight-adjusted rivaroxaban appears to be safe in children. The treatment regimens that we confirmed in children with bodyweights of at least 20 kg and the revised treatment regimens that we predicted in those with bodyweights less than 20 kg will be evaluated in the EINSTEIN-Jr phase 3 trial in children with acute venous thromboembolism. Funding: Bayer AG, Janssen Research and Development.