This paper proposes a joint acoustic echo cancellation (AEC) and speech dereverberation (DR) algorithm in the short-time Fourier transform domain. The reverberant microphone signals are described using an auto-regressive (AR) model. The AR coefficients and the loudspeaker-to-microphone acoustic transfer functions (ATFs) are considered time-varying and are modeled simultaneously using a first-order Markov process. This leads to a solution where these parameters can be optimally estimated using Kalman filters. It is shown that the proposed algorithm outperforms vanilla solutions that solve AEC and DR sequentially and one state-of-the-art joint DRAEC algorithm based on semi-blind source separation, in terms of both speech quality and echo reduction performance.