An apparatus comprises a processing device configured to select, from a first storage virtualization appliance, virtual volumes to migrate to a second storage virtualization appliance. The processing device is also configured to determine a configuration of first storage elements of the first storage virtualization appliance utilized to implement the selected virtual volumes, and to provision second storage elements for implementing the selected virtual volumes on the second storage virtualization appliance, the second storage elements being provisioned in an inactive state. The processing device is further configured to pause input-output operations directed to the selected virtual volumes on the first storage elements, to modify the first storage elements from an active state to the inactive state and the second storage elements from the inactive state to the active state, and to resume input-output operations directed to the selected virtual volumes on the second storage elements of the second storage virtualization appliance.