This paper studies a novel movable antenna (MA)-enhanced multiple-input multiple-output (MIMO) system to leverage the corresponding spatial degrees of freedom (DoFs) for improving the performance of wireless communications. We aim to maximize the achievable rate by jointly optimizing the MA positions and the transmit covariance matrix based on statistical channel state information (CSI). To solve the resulting design problem, we develop a constrained stochastic successive convex approximation (CSSCA) algorithm applicable for the general movement mode. Furthermore, we propose two simplified antenna movement modes, namely the linear movement mode and the planar movement mode, to facilitate efficient antenna movement and reduce the computational complexity of the CSSCA algorithm. Numerical results show that the considered MA-enhanced system can significantly improve the achievable rate compared to conventional MIMO systems employing uniform planar arrays (UPAs) and that the proposed planar movement mode performs closely to the performance upper bound achieved by the general movement mode.