Data Center switches need guarantee high throughput, resiliency and scalability for large-scale networks with constantly floating requirements. Multistage packet switches have been a pervasive solution to implement high-capacity Data Center Networks (DCNs) switches and routers. Yet, classical multistage switching architectures with their Space-Memory variants have shown limited performance. Most proposals prove either too complex to implement or not cost effective. In this paper, we present a highly scalable packet-switch for the DCN environment, in which we exploit the Network-on-Chip (NoC) design paradigm to replace the single-hop crossbars with multi-hop Switching Elements (SEs). In particular, we describe a three-stage switch with Output-Queued Unidirectional NoCs (OQ-UDN) in the central stage of the Clos-network. The design has several advantages over conventional multistage switches. First, it uses a simple Round-Robin (RR) packet dispatching scheme and avoids the need for complex and costly input modules. Besides, it offers better load balancing, a pipelined scheduling and more path-diversity. We assess the performance of the switch in terms of throughput, end-to-end latency and blocking probability using Markov chain analysis, and we propose an analytical model that integrates the various design parameters. Through extensive simulations, we show that the switching architecture achieves high performance under different types of traffic, and that both the analytical and experimental results correlate over wide range of evaluation settings.