A novel approach to stochastic rainfall generation that can reproduce various statistical characteristics of observed rainfall at hourly to yearly timescales is presented. The model uses a seasonal autoregressive integrated moving average (SARIMA) model to generate monthly rainfall. Then, it downscales the generated monthly rainfall to the hourly aggregation level using the Modified Bartlett–Lewis Rectangular Pulse (MBLRP) model, a type of Poisson cluster rainfall model. Here, the MBLRP model is carefully calibrated such that it can reproduce the sub-daily statistical properties of observed rainfall. This was achieved by first generating a set of fine-scale rainfall statistics reflecting the complex correlation structure between rainfall mean, variance, auto-covariance, and proportion of dry periods, and then coupling it to the generated monthly rainfall, which were used as the basis of the MBLRP parameterization. The approach was tested on 34 gauges located in the Midwest to the east coast of the continental United States with a variety of rainfall characteristics. The results of the test suggest that our hybrid model accurately reproduces the first- to the third-order statistics as well as the intermittency properties from the hourly to the annual timescales, and the statistical behaviour of monthly maxima and extreme values of the observed rainfall were reproduced well.