Planning the defossilization of energy systems by facilitating high penetration of renewables and maintaining access to abundant and affordable primary energy resources is a nontrivial multi-objective problem. However, so far, most long-term policies to decrease the carbon footprint of our societies consider the cost of the system as the leading indicator in the energy system models. This paper is the first to develop a novel approach by adding the energy return on investment (EROI) to a whole energy system optimization model. We built the database with all EROI technologies and resources considered. In addition, moving away from fossil-based to carbon-neutral energy systems raises the issue of the uncertainty of low-carbon technologies and resource data. Thus, we conducted a global sensitivity analysis to identify the main parameters driving the variations in the EROI of the system. This novel approach can be applied to any energy system, and we use a real-world case study to illustrate the model: the 2035 ... : Revised version of the paper submitted to Biophysical Economics and Sustainability for a second round of review ...