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Today's data centers are in a constant state of evolution because of equipment refreshes and the move to tiered storage. Data migration is a very important activity in this environment as data moves from one storage device to another without disrupting access from applications. This paper presents the design, implementation, and evaluation of a migration scheme that provides completion time guarantees for a migration task and also minimizes its impact on foreground applications. This scheme is based on an opportunistic data migration scheme that consider migration as background activities. To make sure that a migration task obeys a completion time constraint, an adaptive rate control mechanism is presented. The scheme uses various statistical techniques to estimate system capacities, and utilize these estimates to regulate foreground activities. Trace-driven experimental evaluation shows that our migration scheme is able to ensure that the migration task completes in time while minimizing the impact on foreground application activity.