Epidemic outbreak detection is an important problem in public health and the development of reliable methods for outbreak detection remains an active research area. In this paper we introduce a Bayesian method to detect outbreaks of influenza-like illness from surveillance data. The rationale is that, during the early phase of the outbreak, surveillance data changes from autoregressive dynamics to a regime of exponential growth. Our method uses Bayesian model selection and Bayesian regression to identify the breakpoint. No free parameters need to be tuned. However, historical information regarding influenza-like illnesses needs to be incorporated into the model. In order to show and discuss the performance of our method we analyze synthetic, seasonal, and pandemic outbreak data.