The Paris Agreement aims to address the gap between existing climate policies and policies consistent with ‘holding the increase in global average temperature to well below 2C’. The feasibility of meeting the target has been questioned both in terms of the possible requirement for negative emissions, and ongoing debate on the sensitivity of the climate-carbon cycle system. 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-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 GTC and 307 GTC post-2017 emissions, quantifying spatio-temporal variability of warming, precipitation, ocean acidification and marine productivity. Under rapid decarbonisation 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 (explaining 47% of peak warming uncertainty) becomes unreasonable under strong mitigation conditions.