Hot, cold and dry meteorological extremes are often linked with severe impacts on the public health, agricultural, energy and environmental sectors. Skillful predictions of such extremes could therefore enable stakeholders to better plan and adapt to future impacts of these events. The intensity, duration and frequency of such extremes are affected by anthropogenic climate change and modulated by different modes of climate variability. Here we use a large multi-model ensemble from the Coupled Model Intercomparison Project Phase 6 and constrain these simulations by sub-selecting those members whose global SST anomaly patterns are most similar to observations at a given point in time, thereby phasing in the decadal climate variability with observations. Hot and cold extremes are skillfully predicted over most of the globe, with also a widespread added value from using the constrained ensemble compared to the unconstrained full CMIP6 ensemble. On the other hand, dry extremes show skill only in some regions with results sensitive to the index used. Still, we find skillful predictions and added skill for dry extremes in some regions such as western north America, southern central and eastern Europe, southeastern Australia, southern Africa and the Arabian peninsula. We also find that the added skill in the constrained ensemble is due to a combination of improved multi-decadal variations in phase with observed climate extremes and improved representation of long-term changes. Our results demonstrate that constraining decadal variability in climate projections can provide improved estimates of temperature extremes and drought in the next twenty years, which can inform targeted adaptation strategies to near-term climate change.