Quantifying age structure and tree growth rate of Amazonian forests is essential for understanding their role in the carbon cycle. Here, we use radiocarbon dating and direct measurement of diameter increment to document unexpectedly slow growth rates for trees from three locations spanning the Brazilian Amazon basin. Central Amazon trees, averaging only approximately 1 mm/year diameter increment, grow half as fast as those from areas with more seasonal rainfall to the east and west. Slow growth rates mean that trees can attain great ages; across our sites we estimate 17-50% of trees with diameter >10 cm have ages exceeding 300 years. Whereas a few emergent trees that make up a large portion of the biomass grow faster, small trees that are more abundant grow slowly and attain ages of hundreds of years. The mean age of carbon in living trees (60-110 years) is within the range of or slightly longer than the mean residence time calculated from C inventory divided by annual C allocation to wood growth (40-100 years). Faster C turnover is observed in stands with overall higher rates of diameter increment and a larger fraction of the biomass in large, fast-growing trees. As a consequence, forests can recover biomass relatively quickly after disturbance, whereas recovering species composition may take many centuries. Carbon cycle models that apply a single turnover time for carbon in forest biomass do not account for variations in life strategy and therefore may overestimate the carbon sequestration potential of Amazon forests.