Understanding the microscopic mechanism of Li-ion insertion in intercalation solids is crucial for the design of energy storage devices with optimal power and energy densities. Li intercalation kinetics has been traditionally treated by the phenomenological Butler-Volmer kinetics, but remains poorly measured and understood. For example, reported lithium intercalation kinetics for LiCoO₂ in carbonate-electrolytes vary by 4-5 orders of magnitude. In this study, we developed experimental electrochemical methods for Li⁺-concentration-dependent Tafel kinetic measurements, and showed that the current of intercalation in Li_xCoO₂ and NMCs was proportional to the fraction of empty Li⁺ sites. Exchange current densities and reorganization energies were also extracted for various electrode and electrolyte combinations. These results provide unique experimental evidence to support the microscopic mechanism of Li⁺ intercalation, where the electron and ion transfers are described by the theory of coupled ion-electron transfer (CIET). The proposed ion intercalation mechanism was also validated through the rate-dependent discharge capacity for eight electrode materials including LiFePO₄ and graphite, which decreases linearly with the increasing discharge current under reaction-limited conditions. Our findings suggest that the proposed mechanism applies to a variety of intercalation materials used in energy storage, and governs the power density at low and moderate applied current densities. The possibility of modifying the reaction-limited current with electrodes and electrolytes opens new directions for interfacial engineering of Li-ion batteries.