Simulations from a coupled ice-ocean general circulation model are used to assess the effects on Arctic Ocean freshwater storage of changes in freshwater input through river runoff and precipitation. We employ the climate response function framework to examine responses of freshwater content to abrupt changes in freshwater input. To the lowest order, the response of ocean freshwater content is linear, with an adjustment time scale of approximately 10years, indicating that anomalies in Arctic Ocean freshwater export are proportional to anomalies in freshwater content. However, the details of the transient response of the ocean depend on the source of freshwater input. An increase in river runoff results in a fairly smooth response in freshwater storage consistent with an essentially linear relation between total freshwater content and discharge of excess freshwater through the main export straits. However, the response to a change in precipitation is subject to greater complexity, which can be explained by the localized formation and subsequent export of salinity anomalies which introduce additional response time scales. The results presented here suggest that future increases in Arctic Ocean freshwater input in the form of precipitation are more likely to be associated with variability in the storage and release of excess freshwater than are increases in freshwater input from river runoff. Plain Language Summary This paper shows that the Arctic Ocean adjusts to changes in freshwater input over time scales of about one decade. How much of the added freshwater is stored in the Arctic depends, however, on how the freshwater enters the ocean. If it arrives as additional river runoff, the response in Arctic freshwater storage is relatively smooth and predictable. If it falls, instead, as increased precipitation, the response is less easy to predict because it is complicated by interactions between the ocean and sea ice. This is important because the part of the freshwater that is not stored in the Arctic Ocean is exported to the North Atlantic, where it can affect the global ocean circulation.