Anthropogenic greenhouse gas emissions cause ocean warming and oxygen depletion, with adverse impacts on marine organisms and ecosystems. Warming is one of the main indicators of anthropogenic climate change, but, in the thermocline, changes in oxygen and other biogeochemical tracers may emerge from the bounds of natural variability prior to warming. Here, we assess the time of emergence (ToE) of anthropogenic change in thermocline temperature and thermocline oxygen within an ensemble of Earth system model simulations from the fifth phase of the Coupled Model Intercomparison Project. Changes in temperature typically emerge from internal variability prior to changes in oxygen. However, in about a third (35 +/- 11 %) of the global thermocline deoxygenation emerges prior to warming. In these regions, both reduced ventilation and reduced solubility add to the oxygen decline. In addition, reduced ventilation slows the propagation of anthropogenic warming from the surface into the ocean interior, further contributing to the delayed emergence of warming compared to deoxygenation. Magnitudes of internal variability and of anthropogenic change, which determine ToE, vary considerably among models leading to model-model differences in ToE. We introduce a new metric, relative ToE, to facilitate the multi-model assessment of ToE. This reduces the inter-model spread compared to the traditionally evaluated absolute ToE. Our results underline the importance of an ocean biogeochemical observing system and that the detection of anthropogenic impacts becomes more likely when using multi-tracer observations.