Climate and ecosystem dynamics vary across timescales, but research into climate-driven vegetation dynamics usually focuses on singular timescales. We developed a spectral analysis-based approach that provides detailed estimates of the timescales at which vegetation tracks climate change, from 101 to 105 years. We report dynamic similarity of vegetation and climate even at centennial frequencies (149-1 to 18,012-1 year-1, that is, one cycle per 149 to 18,012 years). A breakpoint in vegetation turnover (797-1 year-1) matches a breakpoint between stochastic and autocorrelated climate processes, suggesting that ecological dynamics are governed by climate across these frequencies. Heightened vegetation turnover at millennial frequencies (4650-1 year-1) highlights the risk of abrupt responses to climate change, whereas vegetation-climate decoupling at frequencies >149-1 year-1 may indicate long-lasting consequences of anthropogenic climate change for ecosystem function and biodiversity.