Reconstructions of Earth's past climate strongly influence our understanding of the dynamics and sensitivity of the climate system. Yet global temperature has been reconstructed for only a few isolated windows of time(1,2), and continuous reconstructions across glacial cycles remain elusive. Here I present a spatially weighted proxy reconstruction of global temperature over the past 2 million years estimated from a multi-proxy database of over 20,000 sea surface temperature point reconstructions. Global temperature gradually cooled until roughly 1.2 million years ago and cooling then stalled until the present. The cooling trend probably stalled before the beginning of the mid-Pleistocene transition(3), and predated the increase in the maximum size of ice sheets around 0.9 million years ago(4-6). Thus, global cooling may have been a precondition for, but probably is not the sole causal mechanism of, the shift to quasi-100,000-year glacial cycles at the mid-Pleistocene transition. Over the past 800,000 years, polar amplification (the amplification of temperature change at the poles relative to global temperature change) has been stable over time, and global temperature and atmospheric greenhouse gas concentrations have been closely coupled across glacial cycles. A comparison of the new temperature reconstruction with radiative forcing from greenhouse gases estimates an Earth system sensitivity of 9 degrees Celsius (range 7 to 13 degrees Celsius, 95 per cent credible interval) change in global average surface temperature per doubling of atmospheric carbon dioxide over millennium timescales. This result suggests that stabilization at today's greenhouse gas levels may already commit Earth to an eventual total warming of 5 degrees Celsius (range 3 to 7 degrees Celsius, 95 per cent credible interval) over the next few millennia as ice sheets, vegetation and atmospheric dust continue to respond to global warming.