Rising atmospheric CO2 concentrations are placing spatially divergent stresses on the world's tropical coral reefs through increasing ocean surface temperatures and ocean acidification. We show how these two stressors combine to alter the global habitat suitability for shallow coral reef ecosystems, using statistical Bioclimatic Envelope Models rather than basing projections on any a priori assumptions of physiological tolerances or fixed thresholds. We apply two different modeling approaches (Maximum Entropy and Boosted Regression Trees) with two levels of complexity (one a simplified and reduced environmental variable version of the other). Our models project a marked temperature-driven decline in habitat suitability for many of the most significant and bio-diverse tropical coral regions, particularly in the central Indo-Pacific. This is accompanied by a temperature-driven poleward range expansion of favorable conditions accelerating up to 40–70 km per decade by 2070. We find that ocean acidification is less influential for determining future habitat suitability than warming, and its deleterious effects are centered evenly in both hemispheres between 5° and 20° latitude. Contrary to expectations, the combined impact of ocean surface temperature rise and acidification leads to little, if any, degradation in future habitat suitability across much of the Atlantic and areas currently considered ‘marginal’ for tropical corals, such as the eastern Equatorial Pacific. These results are consistent with fossil evidence of range expansions during past warm periods. In addition, the simplified models are particularly sensitive to short-term temperature variations and their projections correlate well with reported locations of bleaching events. Our approach offers new insights into the relative impact of two global environmental pressures associated with rising atmospheric CO2 on potential future habitats, but greater understanding of past and current controls on coral reef ecosystems is essential to their conservation and management under a changing climate.