Cost overruns are a significant issue in infrastructure projects, adversely affecting not only economic performance but also sustainability goals by straining resources and extending project timelines. There is consensus among researchers about the persistence of cost overruns and the importance of accurate estimates. However, there are significant differences in the explanation of the reasons for the overruns. While we recognize the importance of understanding the reasons for cost overruns at all stages of project development, we have focused on the reasons for cost overruns after contract award due to the rarely available real and valid data collected at the source of the information. We analyze the deviations between actual and contracted costs, as well as the dependence of cost deviations of individual project types on the size of the contract. For example, the size of the tunnel significantly affects relative cost deviations, while for standard viaducts or road sections this effect is minimal. The results confirmed that cost overruns are less frequent in standard facilities than in those where the experience factor has little influence on the final cost estimate. For example, deviations in the average value of the contracted costs for highway sections range between −12.1% and 27.9% of the contracted value, and for standardized viaduct projects they range between −16.73% and 6.27% of the contracted value. The type of distribution function of deviations between actual and contractually agreed costs was investigated, and a predictive model for estimating future cost deviations of project programs was presented. The goal is to improve economic sustainability and the related optimization of resources in the development of infrastructure, which contributes to the broader agenda of sustainable development. The results encourage the adoption of improved project documentation and forecasting tools, which are essential for sustainable project management.