This paper describes a joint blind source separation and dereverberation method that works adaptively and efficiently in a reverberant noisy environment. The modern approach to blind source separation (BSS) is to formulate a probabilistic model of multichannel mixture signals that consists of a source model representing the time-frequency structures of source spectrograms and a spatial model representing the inter-channel covariance structures of source images. The cutting-edge BSS method in this thread of research is fast multi-channel nonnegative matrix factorization (FastMNMF) that consists of a low-rank source model based on nonnegative matrix factorization (NMF) and a full-rank spatial model based on jointly-diagonalizable spatial covariance matrices. Although FastMNMF is computationally efficient and can deal with both directional sources and diffuse noise simultaneously, its performance is severely degraded in a reverberant environment. To solve this problem, we propose autoregressive FastMNMF (AR-FastMNMF) based on a unified probabilistic model that combines FastMNMF with a blind dereverberation method called weighted prediction error (WPE), where all the parameters are optimized jointly such that the likelihood for observed reverberant mixture signals is maximized. Experimental results showed the superiority of AR-FastMNMF over conventional methods that perform blind dereverberation and BSS jointly or sequentially.