Following the study of migration processes in the continuous domain in Part I of this paper, we reformulate the concept of migration in the discrete domain (Z^m) and define Discrete Migration Processes (DMP). We demonstrate that this model is a natural discrete representation of the continuous model and maintains the model's features in a qualitative sense. We show that under discrete migration any discrete set shrinks to a limit in finitely many iterations. The discrete representation provides an advantageous basis for digitally implementing the MP model. Using this implementation we illustrate the discrete migration of various types of sets under various types of constraints.