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This article investigates the distributed optimization feedback control for a family of multi‐agent systems with external disturbances. For physical implementation in the scenario that only the sampled‐state information is available, a novel disturbance compensation distributed optimization control strategy is proposed by designing a sampled‐data‐based distributed protocol and a sampled‐data‐based disturbance compensator. The disturbances in the current sampling interval are compensated by an exact value at the time in the last sampling interval obtained by using the sampled data. It is proved that the states of agents converge to an arbitrarily small domain of the optimal point of the global cost function if the disturbances and their derivatives are bounded, and the sampling period is short enough. Besides, when disturbances are constants, all the agents' states converge to the optimal point asymptotically. Simulations consolidated the validity of the proposed method. [ABSTRACT FROM AUTHOR]