Emerging evidence indicates that information processing, as well as learning and memory processes, in both the network and single-neuron levels are highly dependent on the correlation structure of multiple spike trains. Contemporary experimental as well as theoretical studies that involve quasi-realistic neuronal stimulation thus require a method for controlling spike train correlations. This letter introduces a general new strategy for generating multiple spike trains with exactly controlled mean firing rates and correlation structure (defined in terms of auto- and cross-correlation functions). Our approach nonlinearly transforms random gaussian-distributed processes with a predistorted correlation structure into nonnegative rate processes, which are then used to generate doubly stochastic Poisson point processes with the required correlation structure. We show how this approach can be used to generate stationary or nonstationary spike trains from small or large groups of neurons with diverse auto- and cross-correlation structures. We analyze and derive analytical formulas for the high-order correlation structure of generated spike trains and discuss the limitations of this approach.