The non-Markovian effect of a fluctuating environment plays an important role in electronic excitation transfer in organic disordered media, such as light-harvesting systems and conjugated polymers. Stochastic Liouville equations (SLE) are used to study the interaction between excitons and the environment. We model the non-Markovian environment phenomenologically with a dichotomic process. An exact approach to solve the SLE based on Shapiro and Loginov's differentiation formulas allows us to rigorously study the effect of the non-Markovian environment on excitation energy transfer, such as coherence conservation and its implication for transfer efficiency. This simple SLE model goes beyond the perturbative second-order master equation valid for both the weak coupling and short time correlation conditions. In addition, we discuss why our non-Markovian model is a good approximation to the SLE model driven by the stationary Gauss Markov process (Ornstein- Uhlenbeck process) over a broad range of fluctuation strengths and correlation times. Numerical results based on our SLE model for dimeric aggregates and the Fenna-Matthews-Olson (FMO) complex reveal the important interplay of intermolecular coupling, correlation time, and fluctuation strength, and their effects on the exciton relaxation process due to the environmental phonon. The results also uncover the connection between localization and motional narrowing, and the efficiency of electronic excitation transfer, demonstrating that the non-Markovian environment is critical for chromophore aggregates to achieve an optimal transfer rate in a noisy environment and to contribute to the robustness of the FMO excitation energy transfer network.