Cloud computing has enabled the Database-as-a-Service (DBaaS) model to manage large volumes of user-generated data using NoSQL data repositories. There are several NoSQL implementations such as document, columnar, and key-value which ensure high availability, fault tolerance and scalability to serve distinct client requirements. Nonetheless, different NoSQL data models may also introduce unnecessary heterogeneity in DBaaS, which further restricts the user to migrate the application services according to business or technology changes. In this paper, we propose a NoSQL data migration framework to foster data portability across cloud-based heterogeneous NoSQL data repositories. The proposed approach involves data standardisation and classification stages to render an efficient mapping, and translation between cloud-based different NoSQL data stores. The current implementation of the framework supports three different data models: document, columnar and graph. Moreover, the framework is meta-model driven, and therefore allows developers to extend the support for new database models. Our approach includes an online compression algorithm for data migration (document to graph) whereby a graph database requires up to 46% less space. There is also a significant reduction (37% to 55%) in the number of nodes in the compressed graph database.