This paper presents the circuit design and magnetic integration of push-pull class-E inverters for wireless power transfer (WPT) up to megahertz. The design criterion for achieving ZVS of a class-E inverter with coupled windings is derived mathematically. The approaches of magnetic integration for push-pull class-E inverters are analyzed and compared. Then, a new magnetic structure with hybrid magnetic materials is proposed to build the integrated inductors with either coupled windings or uncoupled windings. A 3 MHz WPT system is built to verify the analysis. The detailed comparison of the class-E inverters with magnetic integration is presented in terms of switch voltage, efficiency, harmonic currents and thermal distribution. In the optimized design example, the switches keep ZVS over the entire load range without using any closed-loop control. The system efficiency reaches 87.1% at 350 W output power.