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Tropospheric¹⁸O¹⁸O is an emerging proxy for past tropospheric ozone and free‐tropospheric temperatures. The basis of these applications is the idea that isotope‐exchange reactions in the atmosphere drive¹⁸O¹⁸O abundances toward isotopic equilibrium. However, previous work used an offline box‐model framework to explain the¹⁸O¹⁸O budget, approximating the interplay of atmospheric chemistry and transport. This approach, while convenient, has poorly characterized uncertainties. To investigate these uncertainties, and to broaden the applicability of the¹⁸O¹⁸O proxy, we developed a scheme to simulate atmospheric¹⁸O¹⁸O abundances (quantified as ∆₃₆values) online within the GEOS‐Chem chemical transport model. These results are compared to both new and previously published atmospheric observations from the surface to 33 km. Simulations using a simplified O₂isotopic equilibration scheme within GEOS‐Chem show quantitative agreement with measurements only in the middle stratosphere; modeled ∆₃₆values are too high elsewhere. Investigations using a comprehensive model of the O‐O₂‐O₃isotopic photochemical system and proof‐of‐principle experiments suggest that the simple equilibration scheme omits an important pressure dependence to ∆₃₆values: the anomalously efficient titration of¹⁸O¹⁸O to form ozone. Incorporating these effects into the online ∆₃₆calculation scheme in GEOS‐Chem yields quantitative agreement for all available observations. While this previously unidentified bias affects the atmospheric budget of¹⁸O¹⁸O in O₂, the modeled change in the mean tropospheric ∆₃₆value since 1850 CE is only slightly altered; it is still quantitatively consistent with the ice‐core ∆₃₆record, implying that the tropospheric ozone burden increased less than 40% over the twentieth century.