The intensification of extreme weather events under global warming [1] requires the development of tailored evidence-based adaptation and mitigation strategies [2] to reduce the loss and damage caused by these events\cite [3]. Recently, first empirical evidence emerged that extreme weather events can have adverse impacts on economic development for more than a decade [4-7]. The neglect of these long-term effects in state-of-the-art integrated assessment exercises weighing the costs of climate change impacts against the costs of adaptation and mitigation measures may result in a critical lack of ambition in climate action [8]. We here estimate total and country-specific climate change-induced discounted annual damage (DAD) from tropical cyclones (TCs) for a large set of 41 TC-prone countries under different climate and socioeconomic futures. Accounting for the persisting impacts of TCs on the economy, these estimates reveal future adaptation needs of the countries. We then derive temperature-dependent TC damage function for a large set of 41 TC-affected countries that account for persistent growth effects. These functions allow us, for the first time, to quantify the country-level social cost of carbon (SCC) induced by TCs as a key metric to inform mitigation decisions. We find that for a middle-of-the-road scenario regarding greenhouse gas emissions, population development and economic growth, the additional average per-capita DAD corresponds to about one day of annual income lost for the average household in strongly affected high-income countries such as Hong Kong, Taiwan, Japan, the United States but also in TC-prone developing countries as for instance the Philippines or Vietnam. Further, accounting for TC impacts significantly increases the SCC of strongly affected major greenhouse gas emitters such as Japan (+39.8%), China (+8.1%), or the US (+6.3%) as well as globally by +2.1% (+5.4% in TC-affected countries). Our results underline the importance - and pave the way - to adequately account for the impacts of extreme weather events in integrated assessment of remaining climate damages along mitigation and adaptation pathways.