The path-following problem for four-wheel independent driving and four-wheel independent steering electric autonomous vehicles is investigated in this paper. Owing to the over-actuated characters of four-wheel independent driving and four-wheel independent steering autonomous vehicles, a novel yaw rate tracking-based path-following controller is proposed. First, according to the kinematic relationships between vehicle and the reference path, the yaw rate generator is designed by linear matrix inequality theory, with the ability to minimize the disturbances caused by vehicle side slip and varying curvature of path. Considering that the path-following objective and dynamics stability are in conflict with each other in some extreme path-following conditions, a coordinating mechanism based on yaw rate prediction is proposed to satisfy the two conflicting objectives. Then, according to the desired yaw rate and longitudinal velocity, a hierarchical structure is introduced for motion control. The upper-level controller calculates the generalized tracking forces while the allocation layer optimally distributes the generalized forces to tires considering tire vertical load and adhesive utilization. Finally, simulation results indicate that the proposed method can achieve excellent path-following performances in different driving conditions, while both path-following objective and dynamics stability can be satisfied.