Global climate action is urgent, with forest carbon stock critical for mitigating climate change, yet vulnerable to its impacts. However, the long-term dynamics of climate-driven forest carbon stock has not fully been expressed. Here, we introduce the Forest carbon stock Accumulated by Single Tree growth (FAST) framework and constructed a counterfactual scenario to isolate and quantify the impacts of major climatic drivers on forest carbon stock for 1901-2022. Results show that most breakpoints in climate-driven forest carbon stock occurred post-1970, with Europe experiencing the latest, followed by Asia, and North America the earliest. Furthermore, we observe a prevailing increasing trend in climate-driven forest carbon stock, especially in post-breakpoints period (from 53% to 68%), indicating that climate changes have alleviated climatic constraints on forest carbon stocks in most areas. FAST can be utilized for historical, current and future forest carbon stock estimation, providing scientific support for sustainable forest management decisions.