Changes in sea level are driven by a range of natural and anthropogenic forcings. To better understand the response of global mean thermosteric sea-level change to these forcings, we compare three observational datasets to experiments of 28 climate models with up to five different forcing scenarios for 1957–2005. We use the pre-industrial control runs to determine the internal climate variability. Our analysis shows that anthropogenic greenhouse gas and aerosol forcing is required to explain the magnitude of the observed changes, while natural forcing drives most of the externally-forced variability. The experiments that include anthropogenic and natural forcings capture the observed increased trend towards the end of the 20th century best. The observed changes can be explained by scaling the natural-only experiment by 0.70 ± 0.30 and the anthropogenic-only experiment (including opposing forcing from greenhouse gases and aerosols) by 1.08 ± 0.13 (±2σ).