The age, or residence time, of water is a fundamental descriptor of catchment hydrology, revealing information about the storage, flow pathways, and source of water in a single integrated measure. While there has been tremendous recent interest in residence time estimation to characterize watersheds, there are relatively few studies that have quantified residence time at the watershed scale, and fewer still that have extended those results beyond single catchments to larger landscape scales. We examined topographic controls on residence time for seven catchments (0.085–62.4 km²) that represent diverse geologic and geomorphic conditions in the western Cascade Mountains of Oregon. Our primary objective was to determine the dominant physical controls on catchment‐scale water residence time and specifically test the hypothesis that residence time is related to the size of the basin. Residence times were estimated by simple convolution models that described the transfer of precipitation isotopic composition to the stream network. We found that base flow mean residence times for exponential distributions ranged from 0.8 to 3.3 years. Mean residence time showed no correlation to basin area (r² < 0.01) but instead was correlated (r² = 0.91) to catchment terrain indices representing the flow path distance and flow path gradient to the stream network. These results illustrate that landscape organization (i.e., topography) rather than basin area controls catchment‐scale transport. Results from this study may provide a framework for describing scale‐invariant transport across climatic and geologic conditions, whereby the internal form and structure of the basin defines the first‐order control on base flow residence time.