The Brewer–Dobson circulation plays a fundamental role in regulating the transport of trace gases, water vapor, and ozone throughout the stratosphere, yet quantifying changes in its transport efficiency under greenhouse warming remains challenging because no single diagnostic fully characterizes large-scale transport. Here, we develop an integrated diagnostic framework that combines Coupled Model Intercomparison Project Phase 6 climate simulations with Aura Microwave Limb Sounder satellite observations to evaluate changes in Brewer–Dobson circulation transport efficiency. The framework integrates mean age of air, Transformed Eulerian Mean diagnostics, Eliassen–Palm flux divergence, and tracer propagation derived from daily water vapor observations. Multi-model simulations show widespread reductions in mean age of air from the pre-industrial period through future SSP370 projections, indicating progressively younger stratospheric air and enhanced large-scale transport. Dynamical diagnostics reveal strengthened wave-driven residual circulation, with the largest response occurring in the lower stratosphere. Independent satellite observations show coherent tropical-to-extratropical tracer propagation, with the fastest transport occurring within the 400–500 K layer and substantially slower transport above 500 K. Sensitivity analyses using monthly observations and alternative lag thresholds reproduce the same vertical transport hierarchy, demonstrating the robustness of the results. Together, the complementary model and observational diagnostics show that greenhouse-driven changes in the Brewer–Dobson circulation are expressed primarily through enhanced lower-stratospheric transport efficiency rather than major changes in circulation structure. The proposed framework provides a physically consistent approach for evaluating future stratospheric transport and an observational benchmark for assessing climate-model projections.