We propose transmit optimization techniques for multi-input multi-output (MIMO) wiretap channels with statistical channel state information (CSI) at the transmitter. We consider doubly correlated channels towards the legitimate receiver and the eavesdropper. The aim is to maximize the secrecy rates using the knowledge of the channel correlation matrices. We develop gradient-descent based optimization algorithms for obtaining the optimal transmit signals for both Gaussian and finite-alphabet inputs. Furthermore, we introduce a joint precoder and artificial noise (AN) design scheme. We demonstrate the efficacy of the proposed schemes via numerical examples.