The Bayesian Processor of Forecast (BPF) is developed for a continuous predictand. Its purpose is to process a deterministic forecast (a point estimate of the predictand) into a probabilistic forecast (a distribution function, a density function, and a quantile function). The quantification of uncertainty is accomplished via Bayes theorem by extracting and fusing two kinds of information from two different sources: (i) a long sample of the predictand from the National Climatic Data Center, and (ii) a short sample of the official National Weather Service forecast from the National Digital Forecast Database. The official forecast is deterministic and hence deficient: it contains no information about uncertainty. The BPF remedies this deficiency by outputting the complete and well-calibrated characterization of uncertainty needed by decision makers and information providers. The BPF comes furnished with (i) the meta-Gaussian model, which fits well meteorological data as it allows all forms of marginal distribution functions, and non-linear and heteroscedastic dependence structures, and (ii) the statistical procedures for estimation of parameters from asymmetric samples and for coping with nonstationarities in the predictand and the forecast due to the annual cycle and the lead time. A comprehensive illustration of the BPF is reported for forecasts of the daily maximum temperature issued with lead times of 1, 4, and 7 days for three stations in two seasons (cool and warm).