This paper provides a systematic method to build wind speed models based on stochastic differential equations (SDEs). The resulting models produce stochastic processes with a given probability distribution and exponentially decaying autocorrelation function. The only information needed to build the models is the probability density function of the wind speed and its autocorrelation coefficient. Unlike other methods previously proposed in the literature, the proposed method leads to models able to reproduce an exact exponential autocorrelation even if the probability distribution is not Gaussian. A sufficient condition for the property above is provided. The paper includes the explicit formulation of SDE-based wind speed models obtained from several probability distributions used in the literature to describe different wind speed behaviors. All models are validated through numerical simulations. Finally, the proposed procedure is applied to model the wind speed observed at a meteorological station in New Zealand. A comparison of the statistical properties of the wind speed measurements and of the stochastic process generated by the SDE model is also provided. (C) 2016 Published by Elsevier Ltd.