<p>Reaching net-zero CO₂ emissions is expected to halt warming, yet whether temperatures remain stable in the centuries after net-zero is poorly constrained. Models exhibit diverse long-term responses to the cessation of CO₂, including additional multi-century warming. Here we analytically predict this post-cessation temperature change, known as the zero emissions commitment (ZEC), from three climate metrics: the airborne fraction of cumulative CO₂ emissions, transient climate response and equilibrium climate sensitivity. Constraining these metrics implies a near-zero multi-century ZEC from historical CO₂ emissions. Net-zero GHG policies, however, differ from idealized CO₂ cessation by targeting the aggregate effect of multiple GHGs and relying on CO₂ removal to offset residual emissions. To capture these policy-relevant effects, we introduce the net-zero emissions commitment (Net-ZEC). Across scenarios and offsetting conventions, Net-ZEC implies a multi-century cooling of at least 0.6 °C following net-zero GHG emissions.</p>