Online Robust Principle Component Analysis (RPCA) arises naturally in time-varying signal decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Unlike conventional batch RPCA, which processes all the data directly, our method considers a small set of measurements taken per data vector (frame). Moreover, our method incorporates multiple prior information signals, namely previous reconstructed frames, to improve the separation and thereafter, update the prior information for the next frame. Using experiments on synthetic data, we evaluate the separation performance of the proposed algorithm. In addition, we apply the proposed algorithm to online video foreground and background separation from compressive measurements. The results show that the proposed method outperforms the existing methods.