Author summary Seasonal influenza causes a significant public health burden nationwide. Accurate influenza forecasting may help public health officials allocate resources and plan responses to emerging outbreaks. The U.S. Centers for Disease Control and Prevention (CDC) reports influenza data at multiple geographical units, including regionally and nationally, where the national data are by construction a weighted sum of the regional data. In an effort to improve influenza forecast accuracy across all models submitted to the CDC's annual flu forecasting challenge, we examined the effect of imposing this geographical constraint on the set of independent forecasts, made publicly available by the CDC. We developed a novel method to transform forecast densities to obey the geographical constraint that respects the correlation structure between geographical units. This method showed consistent improvement across 79% of models and that held when stratified by targets and test seasons. Our method can be applied to other forecasting systems both within and outside an infectious disease context that have a geographical hierarchy. With an estimated $10.4 billion in medical costs and 31.4 million outpatient visits each year, influenza poses a serious burden of disease in the United States. To provide insights and advance warning into the spread of influenza, the U.S. Centers for Disease Control and Prevention (CDC) runs a challenge for forecasting weighted influenza-like illness (wILI) at the national and regional level. Many models produce independent forecasts for each geographical unit, ignoring the constraint that the national wILI is a weighted sum of regional wILI, where the weights correspond to the population size of the region. We propose a novel algorithm that transforms a set of independent forecast distributions to obey this constraint, which we refer to as probabilistically coherent. Enforcing probabilistic coherence led to an increase in forecast skill for 79% of the models we tested over multiple flu seasons, highlighting the importance of respecting the forecasting system's geographical hierarchy.