In 1967, scientists used a simple climate model to predict that human-caused increases in atmospheric CO₂ should warm Earth's troposphere and cool the stratosphere. This important signature of anthropogenic climate change has been documented in weather balloon and satellite temperature measurements extending from near-surface to the lower stratosphere. Stratospheric cooling has also been confirmed in the mid- to upper stratosphere, a layer extending from roughly 25 to 50 km above Earth’s surface (S_25-50). To date, however, S_25-50 temperatures have not been used in pattern-based attribution studies of anthropogenic climate change. Here we perform the first such "fingerprint" study with satellite-derived patterns of temperature change that extend from the lower troposphere to the upper stratosphere. Including S_25-50 information increases signal-to-noise ratios by a factor of five, markedly enhancing fingerprint detectability. Key features of this global-scale human fingerprint include stratospheric cooling and tropospheric warming at all latitudes, with stratospheric cooling amplifying with height. In contrast, the dominant modes of internal variability in S_25-50 have smaller-scale temperature changes and lack uniform sign. These pronounced spatial differences between S_25-50 signal and noise patterns are accompanied by large cooling of S_25-50 (1-2°C over 1986 to 2022) and low S_25-50 noise levels. Our results explain why extending "vertical fingerprinting" to the mid- to upper stratosphere yields incontrovertible evidence of human effects on the thermal structure of Earth's atmosphere.