In the present work, a new class of high entropy materials for energy storage applications is introduced. Multi-anionic and -cationic compounds are prepared by facile mechanochemistry using a recently designed multi-cationic transition-metal-based high entropy oxide as the precursor and LiF or NaCl as the reactant, leading to formation of lithiated or sodiated materials. Notably, the Li-containing entropy-stabilized oxyfluoride described herein (Lix(Co0.2Cu0.2Mg0.2Ni0.2Zn0.2)OFx) exhibits a working potential of 3.4 V vs. Li+/Li, enabling its use as a cathode active material. Unlike conventional (non-entropy-stabilized) oxyfluorides, this new material shows enhanced Li storage properties due to entropy stabilization, which, in general, facilitates tailoring the cycling performance by varying the constituent elements in yet unprecedented ways. In addition, we demonstrate that the concept of entropy stabilization is also applicable to Na-containing oxychlorides with a rock-salt structure, thus paving the way toward development of (next-generation) post-Li battery technologies.