Knowledge of the evolution of atmospheric carbon dioxide concentrations throughout the Earth's history is important for a reconstruction of the links between climate and radiative forcing of the Earth's surface temperatures. Although atmospheric carbon dioxide concentrations in the early Cenozoic era (about 60 Myr ago) are widely believed to have been higher than at present, there is disagreement regarding the exact carbon dioxide levels, the timing of the decline and the mechanisms that are most important for the control of CO2 concentrations over geological timescales. Here we use the boron-isotope ratios of ancient planktonic foraminifer shells to estimate the pH of surface-layer sea water throughout the past 60 million years, which can be used to reconstruct atmospheric CO2 concentrations. We estimate CO2 concentrations of more than 2,000 p.p.m. for the late Palaeocene and earliest Eocene periods (from about 60 to 52 Myr ago), and find an erratic decline between 55 and 40 Myr ago that may have been caused by reduced CO2 outgassing from ocean ridges, volcanoes and metamorphic belts and increased carbon burial. Since the early Miocene (about 24 Myr ago), atmospheric CO2 concentrations appear to have remained below 500 p.p.m. and were more stable than before, although transient intervals of CO2 reduction may have occurred during periods of rapid cooling approximately 15 and 3 Myr ago.