Atmospheric carbon dioxide records indicate that the land surface has acted as a strong global carbon sink over recent decades, with a substantial fraction of this sink probably located in the tropics, particularly in the Amazon. Nevertheless, it is unclear how the terrestrial carbon sink will evolve as climate and atmospheric composition continue to change. Here we analyse the historical evolution of the biomass dynamics of the Amazon rainforest over three decades using a distributed network of 321 plots. While this analysis confirms that Amazon forests have acted as a long-term net biomass sink, we find a long-term decreasing trend of carbon accumulation. Rates of net increase in above-ground biomass declined by one-third during the past decade compared to the 1990s. This is a consequence of growth rate increases levelling off recently, while biomass mortality persistently increased throughout, leading to a shortening of carbon residence times. Potential drivers for the mortality increase include greater climate variability, and feedbacks of faster growth on mortality, resulting in shortened tree longevity. The observed decline of the Amazon sink diverges markedly from the recent increase in terrestrial carbon uptake at the global scale, and is contrary to expectations based on models.