In many climate change mitigation scenarios, integrated assessment models of the energy and climate systems rely heavily on renewable energy technologies with variable and uncertain generation, such as wind and solar PV, to achieve substantial decarbonization of the electricity sector. However, these models often include very little temporal resolution and thus have difficulty in representing the integration costs that arise from mismatches between electricity supply and demand. The global integrated assessment model, MESSAGE, has been updated to explicitly model the trade-offs between variable renewable energy (VRE) deployment and its impacts on the electricity system, including the implications for electricity curtailment, backup capacity, and system flexibility. These impacts have been parameterized using a reduced-form approach, which allows VRE integration impacts to be quantified on a regional basis. In addition, thermoelectric technologies were updated to include two modes of operation, baseload and flexible, to better account for the cost, efficiency, and availability penalties associated with flexible operation. In this paper, the modeling approach used in MESSAGE is explained and the implications for VRE deployment in mitigation scenarios are assessed. Three important stylized facts associated with integrating high VRE shares are successfully reproduced by our modeling approach: (1) the significant reduction in the utilization of non-VRE power plants; (2) the diminishing role for traditional baseload generators, such as nuclear and coal, and the transition to more flexible technologies; and (3) the importance of electricity storage and hydrogen electrolysis in facilitating the deployment of VRE.