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Natural carbon sinks currently absorb approximately half of the anthropogenic CO₂ emitted by fossil fuel burning, cement production and land-use change. However, this airborne fraction may change in the future depending on the emissions scenario. An important issue in developing carbon budgets to achieve climate stabilisation targets is the behaviour of natural carbon sinks, particularly under low emissions mitigation scenarios as required to meet the goals of the Paris Agreement. A key requirement for low carbon pathways is to quantify the effectiveness of negative emissions technologies which will be strongly affected by carbon cycle feedbacks. Here we find that Earth system models suggest significant weakening, even potential reversal, of the ocean and land sinks under future low emission scenarios. For the RCP2.6 concentration pathway, models project land and ocean sinks to weaken to 0.8 ± 0.9 and 1.1 ± 0.3 GtC yr⁻¹ respectively for the second half of the 21st century and to −0.4 ± 0.4 and 0.1 ± 0.2 GtC yr⁻¹ respectively for the second half of the 23rd century. Weakening of natural carbon sinks will hinder the effectiveness of negative emissions technologies and therefore increase their required deployment to achieve a given climate stabilisation target. We introduce a new metric, the perturbation airborne fraction, to measure and assess the effectiveness of negative emissions.