Unsupervised monocular depth and ego-motion estimation has drawn extensive research attention in recent years. Although current methods have reached a high up-to-scale accuracy, they usually fail to learn the true scale metric due to the inherent scale ambiguity from training with monocular sequences. In this work, we tackle this problem and propose DynaDepth, a novel scale-aware framework that integrates information from vision and IMU motion dynamics. Specifically, we first propose an IMU photometric loss and a cross-sensor photometric consistency loss to provide dense supervision and absolute scales. To fully exploit the complementary information from both sensors, we further drive a differentiable camera-centric extended Kalman filter (EKF) to update the IMU preintegrated motions when observing visual measurements. In addition, the EKF formulation enables learning an ego-motion uncertainty measure, which is non-trivial for unsupervised methods. By leveraging IMU during training, DynaDepth not only learns an absolute scale, but also provides a better generalization ability and robustness against vision degradation such as illumination change and moving objects. We validate the effectiveness of DynaDepth by conducting extensive experiments and simulations on the KITTI and Make3D datasets.