Planning for a green–blue infrastructure system around big cities, having the shape of a belt, to connect natural areas—such as green spaces, water, and agricultural land—is a solution for mitigating the challenges of climate change and urban sprawl. In this context, this study presents an innovative information technology solution for assessing the connectivity of the green and blue areas in the metropolitan area of Bucharest, Romania. The solution is to try to stop the sprawl of Bucharest into the adjacent rural areas and answer the need for a green infrastructure providing ecosystem services. The methodology uses datasets compatible with the European databases on environmental issues, CORINE Land Cover 2018 and Urban Atlas, and two tools in the ArcGIS PRO 2.9 software package, namely Cost Raster and Cost Connectivity. Based on the results, we developed a framework for implementing a strategy for the green–blue infrastructure for the Bucharest metropolitan area. Our methodology is a starter for planning a green–blue belt for the metropolitan area of Bucharest and a model of good practice in terms of making green–blue infrastructure part of urban and territorial planning.