Many studies have sought to constrain climate projections based on recent observations. Until recently, these constraints had limited impact, and projected warming ranges were driven primarily by model outputs. Here, we use the newest climate model ensemble, improved observations, and a new statistical method to narrow uncertainty on estimates of past and future human-induced warming. Cross-validation suggests that our method produces robust results and is not overconfident. We derive consistent observationally constrained estimates of attributable warming to date and warming rate, the response to a range of future scenarios, and metrics of climate sensitivity. We find that historical observations narrow uncertainty on projected future warming by about 50%. Our results suggest that using an unconstrained multimodel ensemble is no longer the best choice for global mean temperature projections and that the lower end of previous estimates of 21st century warming can now be excluded.