Urban greening is an effective mitigation option for climate change in urban areas. In this contribution, a European Union (EU)-wide assessment is presented to quantify the benefits of urban greening in terms of availability of green water, reduction of cooling costs and CO2 sequestration from the atmosphere, for different climatic scenarios. Results show that greening of 35% of the EU's urban surface (i.e. more than 26,000 km2) would avoid up to 55.8 Mtons year-1 CO2 equivalent of greenhouse gas emissions, reducing energy demand for the cooling of buildings in summer by up to 92 TWh per year, with a net present value (NPV) of more than 364 billion Euro. It would also transpire about 10 km3 year-1 of rain water, turning into "green" water about 17.5% of the "blue" water that is now urban runoff, helping reduce pollution of the receiving water bodies and urban flooding. The greening of urban surfaces would decrease their summer temperature by 2.5-6 °C, with a mitigation of the urban heat island effect estimated to have a NPV of 221 billion Euro over a period of 40 years. The monetized benefits cover less than half of the estimated costs of greening, having a NPV of 1323 billion Euro on the same period. Net of the monetized benefits, the cost of greening 26,000 km2 of urban surfaces in Europe is estimated around 60 Euro year-1 per European urban resident. The additional benefits of urban greening related to biodiversity, water quality, health, wellbeing and other aspects, although not monetized in this study, might be worth such extra cost. When this is the case, urban greening represents a multifunctional, no-regret, cost-effective solution.