Current climate policy formulations are largely oblivious to our limited understanding of Earth system processes and potential feedbacks. It is standard practice to design climate policies that assume a well-behaved Earth system, and to estimate their probabilistic outcomes only afterwards (ex-post). However, ensuring the robustness of climate policies requires incorporating physical uncertainty from the onset (ex-ante). These robust policies are not currently part of international discussions, as they have remained confined to stylized academic studies. Here, we employ a new integrated assessment framework that embeds state-of-the-art estimates of physical uncertainty, obtained through Bayesian fusion of the latest data from Earth system models and observations, to derive robust global climate mitigation strategies. Compared to their non-robust counterparts, robust strategies exhibit precautionary measures. Under a variety of cost-benefit and cost-effective experiments, net-zero CO2 emissions must typically be reached a decade earlier, which requires paying a near-term risk premium of 2 to 188 USD per tonne of CO2. On the long term, the precautionary measure consists in developing and sustaining negative emission technologies for centuries. Beyond demonstrating the radical paradigm shift of the ex-ante approach, our work reassesses upwards the challenge humanity faces to build a robustly safe future within Earth system boundaries.