The Reproducibility Checklist provides a lightweight, structured framework to improve transparency and replicability in computational social science research. Instead of a long multi-phase checklist, the final output focuses on essential documentation requirements, data, code, computational environment, and sharing, ensuring that methods are described clearly and can be reused by others. Developed through a systematic literature review and informed by community survey insights, the checklist reflects the practical needs of researchers while avoiding unnecessary complexity. Integrated directly into the Methods Hub submission workflow and guidelines, it standardises how computational methods are documented and evaluated. The checklist was validated through user studies and an experimental evaluation, demonstrating improved reproducibility outcomes compared with external repositories. Workshops and training modules further support adoption. By using this tool, researchers can improve methodological rigour, strengthen trust in their results, and contribute to a culture of openness and reliability in computational social science.