A method comprises receiving an input specifying one or more rules for archiving a plurality of files from a source storage location to a target storage location, wherein the target storage location comprises a cloud storage platform comprising a plurality of storage classes. In the method, one or more of the plurality of files are retrieved from the source storage location for migration to the target storage location based at least in part on the one or more rules. Assignment of the one or more of the plurality of files to respective ones of the plurality of storage classes is controlled based at least in part on the one or more rules. The one or more rules specify one or more constraints for the assignment of the one or more of the plurality of the files to the respective ones of the plurality of storage classes.