Logical reorganization of data and requirements of differentiated QoS in information systems necessitate bulk data migration by the underlying storage layer. Such data migration needs to ensure that regular client I/Os are not impacted significantly while migration is in progress. We formalize the data migration problem in a unified admission control framework that captures both the performance requirements of client I/Os and the constraints associated with migration. We propose an adaptive rate-control based data migration methodology, QoSMig, that achieves the optimal client performance in a differentiated QoS setting, while ensuring that the specified migration constraints are met. QoSMig uses both long term averages and short term forecasts of client traffic to compute a migration schedule. We present an architecture based on Service Level Enforcement Discipline for Storage (SLEDS) that supports QoSMig. Our trace-driven experimental study demonstrates that QoSMig provides significantly better I/O performance as compared to existing migration methodologies.