The Paris Agreement of December 2015 stated a goal to pursue efforts to keep global temperatures below 1.5°C above preindustrial levels and well below 2°C. The IPCC was charged with assessing climate impacts at these temperature levels, but fully coupled equilibrium climate simulations do not currently exist to inform such assessments. In this study, we produce a set of scenarios using a simple model designed to achieve long-term 1.5 and 2°C temperatures in a stable climate. These scenarios are then used to produce century-scale ensemble simulations using the Community Earth System Model, providing impact-relevant long-term climate data for stabilization pathways at 1.5 and 2°C levels and an overshoot 1.5°C case, which are realized (for the 21st century) in the coupled model and are freely available to the community. Here we describe the design of the simulations and a brief overview of their impact-relevant climate response. Exceedance of historical record temperature occurs with 60% greater frequency in the 2°C climate than in a 1.5°C climate aggregated globally, and with twice the frequency in equatorial and arid regions. Extreme precipitation intensity is statistically significantly higher in a 2.0°C climate than a 1.5°C climate in some specific regions (but not all). The model exhibits large differences in the Arctic, which is ice-free with a frequency of 1 in 3 years in the 2.0°C scenario, and 1 in 40 years in the 1.5°C scenario. Significance of impact differences with respect to multi-model variability is not assessed.