  The expansion of the Universe leads to a rapid drop in the mean hydrogen
Ly-alpha opacity tau of the intergalactic medium (IGM), tau (1+z)^{3.8},
between redshifts 4 and 3. Measurements of the temperature evolution of the IGM
and of the He II opacity both suggest that He II reionizes in this redshift
range. We use hydrodynamical simulations to show that the temperature increase
associated with He II reionization leads to a relatively sudden decrease in tau
around the reionization epoch of ~ 10 per cent. We find clear evidence for such
a feature in the evolution of tau determined from a sample of ~ 1100 quasars
obtained from the SDSS. He II reionization starts at redshift ~ 3.4, and lasts
for (Delta z) ~ 0.4. The increase in the IGM temperature also explains the
widths of hydrogen absorption lines as measured in high-resolution spectra.
