This paper introduces a novel data-driven motion in-betweening system to reach target poses of characters by making use of phases variables learned by a Periodic Autoencoder. Our approach utilizes a mixture-of-experts neural network model, in which the phases cluster movements in both space and time with different expert weights. Each generated set of weights then produces a sequence of poses in an autoregressive manner between the current and target state of the character. In addition, to satisfy poses which are manually modified by the animators or where certain end effectors serve as constraints to be reached by the animation, a learned bi-directional control scheme is implemented to satisfy such constraints. The results demonstrate that using phases for motion in-betweening tasks sharpen the interpolated movements, and furthermore stabilizes the learning process. Moreover, using phases for motion in-betweening tasks can also synthesize more challenging movements beyond locomotion behaviors. Additionally, style control is enabled between given target keyframes. Our proposed framework can compete with popular state-of-the-art methods for motion in-betweening in terms of motion quality and generalization, especially in the existence of long transition durations. Our framework contributes to faster prototyping workflows for creating animated character sequences, which is of enormous interest for the game and film industry.