This paper provides a systematic three-stage methodology for migrating complex real-time industrial software systems from single-core to multi-core computing platforms. Single-core platforms have limited computational capabilities that prevent integration of computationally demanding applications such as image processing within the existing system. Modern multi-core processors provide increased computing capacity and allow the parallel execution of different applications within the system. However, this transition is non-trivial and requires a systematic and well-defined migration process. This paper reviews some of the existing migration methods and provides a systematic multi-phase migration process with emphasis on software architecture recovery and transformation to explicitly address the timing and dependability attributes expected of industrial software systems.