Cloud and Grid computing share some essential driving ideas although the computing and economic models are very different. In this paper, we propose different strategies for the Batch-oriented and Service-oriented computing models interoperability. In particular, we describe an innovative approach to connect together Computational Grids and IaaS providers. This is achieved via introducing a simple and powerful DBMS-based system of deploying VM images from a Cloud environment in order to fulfill particular requests of task execution coming from a Grid environment. From a user point of view, resource authorization and access are kept unchanged, thus preserving the user experience related to the Grid. From the accounting point of view, in order to inform the Grid sites that a certain resource is available on a given Cloud-enabled Grid site, the information is published on the Grid information system. In this so-delineated scenario, we are able of using the powerful capability of distributing jobs of the Grid in order to allocate resources not only belonging to Grid clusters, but also with different architectures like GPUs, FPGAs and other systems. The target DBMS-based system has been designed for orchestrate a set of computing systems able to provide physical and virtual resources, creating a unified system, in which the various users-submitted computing tasks are managed and optimized. The goodness of the proposed system is demonstrated by a series of experiments highlighting the benefits of our approach.