Hydrogen (H2) energy has a high potential to become a source of future sustainable fuel to replace fossil fuel. At present, natural gas conversion is the conventional process to produce H2. However, this process produces carbon dioxide (CO2) emissions as a by-product. CO2 capture, utilisation, and storage (CCUS) technologies can be integrated in conventional H2 plants to address this issue. By doing so, conventional H2 plants can be retrofitted to produce cleaner H2 called blue H2. This work presents a mathematical model to optimise blue H2 processes integrated with CCUS technologies. The research objectives are to determine optimal and feasible decarbonisation systems for H2 production and optimal storage technologies for the produced H2 with minimum cost. The developed optimisation-based model considers different grey H2 processes, CO2 capture technologies, CO2 transportation, utilisation, storage, and H2 storage. The model factors technology efficiency, costing and overall energy consumption. The developed model is demonstrated with a blue H2 production case study. The optimised blue H2 process with CCUS was obtained with the optimisation objective of minimising total annualised cost (TAC).