Records of solar and lunar eclipses in the period 700 BC to AD 1600, originating from the ancient and medieval civilizations of Babylon, China, Europe and the Arab world, are amassed and critically appraised for their usefulness in answering questions about the long-term variability of the Earth's rate of rotation. Results from previous analyses of lunar occultations in the period AD 1600-1955.5, and from high-precision data in AD 1955.5-1990, are included in the dataset considered in this paper. Using the change in the length of the mean solar day (l.o.d.) in units of milliseconds per century (ms cy^-1) as the measure of acceleration in the rate of rotation, it is found that the l.o.d. has increased by (+1.70 ± 0.05) ms cy^-1 ($\equiv $ (-4.5 ± 0.1) × 10^-22 rad s^-2) on average over the past 2700 years. Yet an increase of +2.3 ± 0.1 ms cy^-1 ($\equiv $ (-6.1 ± 0.4) × 10^-22 rad s^-2) is expected from the tidal braking of the Earth's spin, assuming a value of -26.0^{′ ′} cy^-2 for the tidal acceleration of the Moon. There is thus an average accelerative component in the Earth's rotation which acts to decrease the l.o.d. by (-0.6 ± 0.1) ms cy^-1 ($\equiv $ (+1.6 ± 0.4) × 10^-22 rad s^-2). Moreover, it is shown that besides this accelerative component, there is a fluctuation in the l.o.d. with a semi-amplitude of ∼ 4 ms and a period of ∼ 1500 yr.