This study considers the output consensus problem of high‐order leader‐following multi‐agent systems with unknown non‐linear dynamics, in which the delayed and sampled outputs of the system are the only available data. The unknown non‐linear dynamics are assumed to satisfy the Lipschitz condition and the interconnected topologies are assumed to be undirected and connected. A distributed observer‐based output feedback controller is proposed for the system to reach output consensus. Both of the bounds of the allowable delay and sampling period are also obtained. Stability analysis shows that the considered systems are globally exponentially stable under the output feedback controller. Finally, a simulation example is given to validate our theoretical results.