The crucial role of networking in Cloud computing calls for federated management of both computing and networking resources for end-to-end service provisioning. Application of the Service-Oriented Architecture (SOA) in both Cloud computing and networking enables a convergence of network and Cloud service provisioning. One of the key challenges to network - Cloud convergence lies in QoS-aware composition of network and Cloud services. In this paper, we propose a QoS-aware service composition method to tackle this challenging issue. We first present a system model for network - Cloud service composition and formulate the service composition problem as a variant of Multi-Constrained Optimal Path (MCOP) problem. We then develop an algorithm to solve the problem and give theoretical analysis on properties of the algorithm to show its effectiveness and efficiency for QoS-aware network-Cloud service composition. Performance of the proposed algorithm is evaluated through extensive simulation experiments and the obtained results indicate that the proposed method achieves better performance in service composition than the best currently available MCOP approach.