We investigate cooperative output regulation (COR) for heterogeneous multi-agent systems (MASs), aimed at synchronizing the outputs of all agents to the desired reference trajectory in the presence of the disturbance, which are both deterministic and generated from an exosystem. First we study the single-agent problem, which coincides with the output regulation under unity output feedback. A new state-space solution, applicable to multi-input/multi-output systems, is derived and presented. The COR is then studied for heterogeneous MASs based on the relative output measurements, assuming that the reference trajectory is transmitted to one or more agents. We show how the feedback MAS can be designed to achieve both the internal stability and COR when the feedback graphs contain directed spanning trees. A simulation example is worked out to illustrate the proposed design method.