APPARATUS, METHOD AND COMPUTER PROGRAM PRODUCT FOR CONTROLLED ORDERING OF DATA PAGES FOR MIGRATION FROM SOURCE STORAGE SYSTEM INTO TARGET STORAGE SYSTEM

An apparatus in an illustrative embodiment comprises at least one processing device comprising a processor coupled to a memory. The processing device is configured to identify a storage volume to be migrated from a source storage system to a target storage system, and to issue one or more commands to at least one of the source storage system and a host device as part of a migration session for the storage volume. Responsive to the one or more commands, a plurality of data pages are received, with the data pages having respective hash values that are computed based at least in part on a native page size of the target storage system as specified in at least one of the one or more commands. The one or more commands illustratively comprise a plurality of read next page commands, with a given one of the read next page commands including information identifying the storage volume, the native page size of the target storage system, and the migration session.