State-of-the-art climate models now include more climate processes which are simulated at higher spatial resolution than ever1. Nevertheless, some processes, such as atmospheric chemical feedbacks, are still computationally expensive and are often ignored in climate simulations1,2. Here we present evidence that how stratospheric ozone is represented in climate models can have a first order impact on estimates of effective climate sensitivity. Using a comprehensive atmosphere-ocean chemistry-climate model, we find an increase in global mean surface warming of around 1°C (~20%) after 75 years when ozone is prescribed at pre-industrial levels compared with when it is allowed to evolve self-consistently in response to an abrupt 4×CO2 forcing. The difference is primarily attributed to changes in longwave radiative feedbacks associated with circulation-driven decreases in tropical lower stratospheric ozone and related stratospheric water vapour and cirrus cloud changes. This has important implications for global model intercomparison studies1,2 in which participating models often use simplified treatments of atmospheric composition changes that are neither consistent with the specified greenhouse gas forcing scenario nor with the associated atmospheric circulation feedbacks3-5.