Various businesses and industries such as financial, medical care management, supply chain management, data management, Internet of Things (IoT) and government supremacy, have been using blockchain technology to develop systems. During the selection of blockchain platforms, many criteria need to be taken into account depending on the organization, project and use case requirements. This study proposes a systematic selection method based on the Fuzzy AHP-TOPSIS approach which compares and selects alternative blockchain platforms against a set of selection criteria that cover both features and non-functional properties. A case study was conducted to evaluate the applicability of the proposed selection method. The proposed selection method which consists of three main stages was applied for the comparison and selection of the most appropriate blockchain platform for two projects. In the case study, three blockchain platforms were selected and ranked for each project based on selection criteria derived from the project requirements. Both project representatives showed strong agreement with the applicability aspects of the proposed selection method. It is concluded that the proposed selection criteria and selection method can be applied practically to support the decision-makers in blockchain platform selection for real-world projects.