Over the last few years, Autonomic Computing has been a key enabler for Cloud system's dynamic adaptation. However, autonomously managing complex systems (such as in the Cloud context) is not trivial and may quickly become fastidious and error-prone. We advocate that Cloud artifacts, regardless of the layer carrying them, share many common characteristics. Thus, this makes it possible to specify, (re)configure and monitor them in an homogeneous way. To this end, we propose a generic model-based architecture for allowing the autonomic management of any Cloud system. From a " XaaS " model describing a given Cloud system, possibly over multiple layers of the Cloud stack, Cloud administrators can derive an autonomic manager for this system. This paper introduces the designed model-based architecture, and notably its core generic XaaS modeling language. It also describes the integration with a constraint solver to be used by the autonomic manager , as well as the interoperability with a Cloud standard (TOSCA). It presents an implementation (with its application on a multi-layer Cloud system) and compares the proposed approach with other existing solutions.