This article formulates a fully-distributed and delay-tolerant secondary control scheme for droop-controlled AC microgrids. The proposed strategy is inspired by the cooperative control concept of multi-agent systems (MASs). It considers the hierarchical control structure of the distributed energy resource (DER) units. It ensures equal active power sharing between three DER units, where each unit tracks the time-varying average load, with a finite-time convergence. As a result, the frequencies of the DER units are regulated to their nominal values. Furthermore, it offers plug-and-play capability for DER units, demonstrates significant robustness against load disturbances, and successfully tolerates, small as well as large, communication time-delays. Due to the fully-distributed configuration of the proposed control strategy, each DER unit in the test microgrid requires only its own information and information of its neighbors. The benefit is two-fold: not only this configuration assists in minimizing the overall bandwidth requirement, and cost of the corresponding communication network, but also it increases the reliability of the microgrid operation. The performance and effectiveness of the proposed technique is supported by exhaustive numerical simulations performed in Matlab/Simulink on an AC microgrid testbench comprising three DER units. The proposed strategy renders the superior performance in several aspects as compared to the existing developments in the literature in this area.