Climate change and inequality are critical and interrelated issues. Despite growing empirical evidence on the distributional implications of climate policies and climate risks, mainstream model-based assessments are often silent on the interplay between climate change and economic inequality. Here we fill this gap through an ensemble of eight large-scale integrated assessment models that belong to different economic paradigms and feature income heterogeneity. We quantify the distributional implications of climate impacts and of the varying compensation schemes of climate policies compatible with the goals of the Paris Agreement. By 2100, climate impacts will increase inequality by 1.4 points of the Gini index on average. Maintaining global mean temperature below 1.5 °C reduces long-term inequality increase by two-thirds but increases it slightly in the short term. However, equal per-capita redistribution can offset the short-term effect, lowering the Gini index by almost two points. We quantify model uncertainty and find robust evidence that well-designed policies can help stabilize climate and promote economic inclusion.