Open Science is widely regarded as a culture that is characterised by the transparency and broad accessibility of scholarly work, where researchers share openly artefacts almost immediately and with a very wide audience. The overarching aim of this paper is to document the systematic development of a European postgraduate programme on Open Science and Research Data Management developed by the TRAINRDM project. TRAINRDM is a 30-month European Union funded project, which aims to develop a training network around Open Science and Research Data Management. We have applied a comprehensive survey collecting 239 responses from researchers across Europe, representative of 2.58 million individuals i.e. the total number of researchers employed in the EU-27 region. We then mapped out existing skills and offerings at different TRAIN-RDM partner institutions to produce a fully-online postgraduate programme with micro-credentials, fully distributed delivery, and compliance to FAIR principles to address academic and industrial research needs. The main outputs of the project are a training programme for Early Career Researchers delivered in Summer 2022, and a the postgraduate programme (Master degree) to be fully validated under the European Qualifications Framework at Level 7 and delivered in 2023. The TRAINRDM curricula, teaching materials, data, and software are openly released under CC BY 4.0 and GPL licenses.