With the rapid evolution of technological, economic, and regulatory landscapes, contemporary blockchain platforms are all but certain to undergo major changes. Therefore, the applications that rely on them will eventually need to migrate from one blockchain instance to another to remain competitive and secure, as well as to enhance the business process, performance, cost efficiency, privacy, and regulatory compliance. However, the differences in data and smart contract representations, modes of hosting, transaction fees, as well as the need to preserve consistency, immutability, and data provenance introduce unique challenges over database migration. We first present a set of blockchain migration scenarios and data fidelity levels using an illustrative example. We then present a set of migration patterns to address those scenarios and the above data management challenges. Finally, we demonstrate how the effort, cost, and risk of migration could be minimized by choosing a suitable set of data migration patterns, data fidelity level, and proactive system design. Practical considerations and research challenges are also highlighted.