Precipitation extremes have increased in many regions of the United States, suggesting that climate change may be exacerbating the cost of flooding. However, the impact of historical precipitation change on the cost of US flood damages remains poorly quantified. Applying empirical analysis to historical precipitation and flood damages, we estimate that approximately one-third (36%) of the cost of flood damages over 1988 to 2017 is a result of historical precipitation changes. Climate models show that anthropogenic climate change has increased the probability of heavy precipitation associated with these costs. Our results provide information quantifying the costs of climate change, and suggest that lower levels of future warming would very likely reduce flooding losses relative to the current global warming trajectory.