We integrate life cycle indicators for various technologies of an energy system model with high spatiotemporal detail and a focus on Europe and North Africa. Using multi-objective optimization, we calculate a pareto front that allows us to assess the trade-offs between system costs and life cycle greenhouse gas (GHG) emissions of future power systems. Furthermore, we perform environmental ex-post assessments of selected solutions using a broad set of life cycle impact categories. In a system with the least life cycle GHG emissions, the costs would increase by ~63%, thereby reducing life cycle GHG emissions by ~82% compared to the cost-optimal solution. Power systems mitigating a substantial part of life cycle GHG emissions with small increases in system costs show a trend towards a deployment of wind onshore, electricity grid and a decline in photovoltaic plants and Li-ion storage. Further reductions are achieved by the deployment of concentrated solar power, wind offshore and nuclear power but lead to considerably higher costs compared to the cost-optimal solution. Power systems that mitigate life cycle GHG emissions also perform better for most impact categories but have higher ionizing radiation, water use and increased fossil fuel demand driven by nuclear power. This study shows that it is crucial to consider upstream GHG emissions in future assessments, as they represent an inheritable part of total emissions in ambitious energy scenarios that, so far, mainly aim to reduce direct CO2 emissions.