With the rapid evolution of technological, economic, and regulatory landscapes, contemporary Blockchian platforms are all but certain to undergo major changes. Therefore, applications that rely on them will eventually need to migrate the Blockchain to remain competitive and secure, as well as to enhance the performance, cost efficiency, privacy, and regulatory compliance. However, the differences in data and smart contract representations, mode of hosting, transaction fees, and 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 derive a set of migration patterns to address those scenarios and above data management challenges. Finally, we demonstrate how the effort, cost, and risk of Blockchain migration can be minimized by choosing a suitable data fidelity level and proactive system design. Practical considerations and several research challenges are also highlighted.