Tropospheric ¹⁸O¹⁸O 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 drive ¹⁸O¹⁸O abundances toward isotopic equilibrium. However, previous work used an offline box-model framework to explain the ¹⁸O¹⁸O 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 the ¹⁸O¹⁸O proxy, we developed a scheme to simulate atmospheric ¹⁸O¹⁸O abundances (quantified as ∆₃₆ values) 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 O₂ isotopic equilibration scheme within GEOS-Chem show quantitative agreement with measurements only in the middle stratosphere; modeled ∆₃₆ values are too high elsewhere. Investigations using a comprehensive model of the O-O₂-O₃ isotopic photochemical system and proof-of-principle experiments suggest that the simple equilibration scheme omits an important pressure dependence to ∆₃₆ values: the anomalously efficient titration of ¹⁸O¹⁸O to form ozone. Incorporating these effects into the online ∆₃₆ calculation scheme in GEOS-Chem yields quantitative agreement for all available observations. While this previously unidentified bias affects the atmospheric budget of ¹⁸O¹⁸O in O₂, the modeled change in the mean tropospheric ∆₃₆ value since 1850 C.E. is only slightly altered; it is still quantitatively consistent with the ice-core ∆₃₆ record, implying that the tropospheric ozone burden increased less than ~40% over the twentieth century.