This paper investigates the consensus disturbance rejection problem among multiple high-order agents with directed graphs. Based on disturbance observers, distributed consensus dis-turbance rejection protocols are constructed in leaderless and leader-follower consensus setups. Dif-ferent from the previous related papers, the consensus protocols in this paper are developed in a fully distributed fashion, relying on only the state information of each agent and its neighbors. Suf-ficient conditions are provided to guarantee that the asymptotic stability of high-order multi-agent systems can be reached with matched disturbances.