Cloud computing enables a transparent access to information technology (IT) services such that the users do not need to know the location and characteristics of the relevant resources. While IT resource virtualization and service abstraction have been widely investigated, data transport within the cloud and its efficient control have not received much attention in the technical literature. In fact, connectivity is, itself, a service that contributes to the overall performance of the cloud. This paper introduces a novel classification of the Network as a Service (NaaS) such that it can be orchestrated with other cloud services. Then, it proposes a network virtualization platform (NVP) as the mediation layer able to provide NaaS to cloud computing by exploiting the functionality provided by control plane (CP)-enabled networks. In particular, the proposed NVP maps the end-point addresses and perceived Quality of Service parameters of a NaaS requests in the parameters characterizing the connectivity as viewed by transport networks using the information obtained from the CP at the boundary of the network. The NVP uses these parameters to fulfill connectivity requests to the CP. Finally, this paper presents a complete design from both the software implementation and network signaling perspective of two use cases in which NaaS is involved as stand-alone facility for the connectivity service provisioning or is combined with other cloud services for a storage service provisioning.