During the last decade we have seen an explosive growth in the deployment of cloud applications and services. In this context, one of the challenges is Quality of Service (QoS) management, which is the problem of allocating resources to the applications to guarantee a service level along dimensions such as performance, availability and reliability. Compared with the traditional best-effort service model based on BGP and the classical tunnelling alternatives (like MPLS), software-defined-networking (SDN) has the potential to provide a better QoS guarantee for cloud applications and services due to its centralized control, network-wide monitoring and flow-level scheduling. With this in mind, we propose a QoS-aware overlay routing based on the SDN architecture, which consists on the rewriting of IP address and TCP/UDP ports in order to be able to force the packets to follow the desired path on the overlay. We evaluate the proposal through both simulations and practical implementation analysis. In particular, we test our solution using two of the most popular SDN controllers: ONOS and OpenDayLight.