This dissertation focuses on the introduction and development of an integrated model-based design and optimization platform to solve the optimal design and optimal control, or hardware and software co-design, problem for hybrid electric propulsion systems. Specifically, the hybrid and plug-in hybrid electric powertrain systems with diesel and natural gas (NG) fueled compression ignition (CI) engines and large Li-ion battery energy storage system (ESS) for propelling a hybrid electric marine vessel are investigated. The combined design and control optimization of the hybrid propulsion system is formulated as a bi-level, nested optimization problem. The lower-level optimization applies dynamic programming (DP) to ensure optimal energy management for each feasible powertrain system design, and the upper-level global optimization aims at identifying the optimal sizes of key powertrain components for the powertrain system with optimized control. Recently, Li-ion batteries became a promising ESS technology for electrified transportation applications. However, these costly Li-ion battery ESSs contribute to a large portion of the powertrain electrification and hybridization costs and suffer a much shorter lifetime compared to other key powertrain components. Different battery performance modelling methods are reviewed to identify the appropriate degradation prediction approach. Using this approach and a large set of experimental data, the performance degradation and life prediction model of LiFePO4 type battery has been developed and validated. This model serves as the foundation for determining the optimal size of battery ESS and for optimal energy management in powertrain system control to achieve balanced reduction of fuel consumption and the extension of battery lifetime. In modelling and design of different hybrid electric marine propulsion systems, the life cycle cost (LCC) model of the cleaner, hybrid propulsion systems is introduced, considering the investment, replacement and operational costs of their major contributors. The costs of liquefied NG (LNG), diesel and electricity in the LCC model are collected from various sources, with a focus on present industrial price in British Columbia, Canada. The greenhouse gas (GHG) and criteria air pollutant (CAP) emissions from traditional diesel and cleaner NG-fueled engines with conventional and optimized hybrid electric powertrains are also evaluated. To solve the computational expensive nested optimization problem, a surrogate model-based (or metamodel-based) global optimization method is used. This advanced global optimization search algorithm uses the optimized Latin hypercube sampling (OLHS) to form the Kriging model and uses expected improvement (EI) online sampling criterion to refine the model to guide the search of global optimum through a much-reduced number of sample data points from the computationally intensive objective function. Solutions from the combined hybrid propulsion system design and control optimization are presented and discussed. This research has further improved the methodology of model-based design and optimization of hybrid electric marine propulsion systems to solve complicated co-design problems through more efficient approaches, and demonstrated the feasibility and benefits of the new methods through their applications to tugboat propulsion system design and control developments. The resulting hybrid propulsion system with NG engine and Li-ion battery ESS presents a more economical and environmentally friendly propulsion system design of the tugboat. This research has further improved the methodology of model-based design and optimization of hybrid electric marine propulsion systems to solve complicated co-design problems through more efficient approaches, and demonstrated the feasibility and benefits of the new methods through their applications to tugboat propulsion system design and control developments. Other main contributions include incorporating the battery performance degradation model to the powertrain size optimization and optimal energy management; performing a systematic design and optimization considering LCC of diesel and NG engines in the hybrid electric powertrains; and developing an effective method for the computational intensive powertrain co-design problem.