Climate models predict a dramatic increase in the annual frequency and severity of extreme weather events during the next century. Here we show that increases in the annual frequency of severe storms lead to a decrease in the diversity and complexity of food webs of giant kelp forests, one of the most productive habitats on Earth. We demonstrate this by linking natural variation in storms with measured changes in kelp forest food web structure in the Santa Barbara Channel using structural equation modeling (SEM). We then match predictions from statistical models to results from a multiyear kelp removal experiment designed to simulate frequent large storms. Both SEM models and experiments agree: if large storms remain at their current annual frequency (roughly one major kelp-removing storm every 3.5 years), periodic storms help maintain the complexity of kelp forest food webs. However, if large storms increase in annual frequency and begin to occur year after year, kelp forest food webs become less diverse and complex as species go locally extinct. The loss of complexity occurs primarily due to decreases in the diversity and complexity of higher trophic levels. Our findings demonstrate that shifts in climate-driven disturbances that affect foundation species are likely to have impacts that cascade through entire ecosystems.