Soft-switching self-tuning H-bridge converters for inductive power transfer (IPT) systems with resonant current regulation are introduced. The proposed converters are controlled based on an amplitude modulation technique for resonant converters to regulate the transferred power in an IPT system. The switching operations of the converters are synchronized to the resonance current of the IPT system which in turn eliminates the need for manual frequency tuning and enables soft-switching operations (zero-current switching). Soft-switching operations increase the efficiency and reliability, and reduce the switching stress and electromagnetic interference (EMI) of the converter. Based on the control design, a simplified digital control circuit is proposed which can be used as an alternative for high-cost DSP/FPGA solutions. The design methodology, theoretical analysis of the proposed converter, along with simulation and experimental results on a case study IPT system are presented in detail. The results show that the proposed converters can effectively regulate the transferred power with self-tuning capability and soft-switching operation.