We present total cross sections for single and double ionization of helium by antiproton impact over a wide range of impact energies from 10 keV/amu to 1 MeV/amu. A nonperturbative time-dependent close-coupling method is applied to fully treat the correlated dynamics of the ionized electrons. Excellent agreement is obtained between our calculations and experimental measurements of total single and double ionization cross sections at high impact energies, whereas for lower impact energies, some discrepancies with experiment are found. At an impact energy of 1 MeV we also find that the double-to-single ionization ratio is twice as large for antiproton impact as for proton impact, confirming a long-standing unexpected experimental measurement.