The Paris Agreement 1 aims to address the gap between existing climate policies and policies consistent with "holding the increase in global average temperature to well below 2 C". The feasibility of meeting the target has been questioned both in terms of the possible requirement for negative emissions 2 and ongoing debate on the sensitivity of the climate-carbon-cycle system 3. Using a sequence of ensembles of a fully dynamic three-dimensional climate-carbon-cycle model, forced by emissions from an integrated assessment model of regional-level climate policy, economy, and technological transformation, we show that a reasonable interpretation of the Paris Agreement is still technically achievable. Specifically, limiting peak (decadal) warming to less than 1.7 °C, or end-of-century warming to less than 1.54 °C, occurs in 50% of our simulations in a policy scenario without net negative emissions or excessive stringency in any policy domain. We evaluate two mitigation scenarios, with 200 gigatonnes of carbon and 307 gigatonnes of carbon post-2017 emissions respectively, quantifying the spatio-temporal variability of warming, precipitation, ocean acidification and marine productivity. Under rapid decarbonization decadal variability dominates the mean response in critical regions, with significant implications for decision-making, demanding impact methodologies that address non-linear spatio-temporal responses. Ignoring carbon-cycle feedback uncertainties (which can explain 47% of peak warming uncertainty) becomes unreasonable under strong mitigation conditions.