During the last one million years, ice ages occurred with a dominant periodicity of 100 kyr (1 kyr = 1,000 years), while the solar radiation variability resulting from astronomical forcing is concentrated at higher frequencies and shows negligibly small power around this time scale. Although many promising frameworks have been introduced to solve this 100-kyr problem, a comprehensive theory of glacial cycles remains elusive. Here we show, using an Earth System Model of intermediate complexity, that the 100-kyr glacial cycles can be explained via a phenomenon called vibrational resonance. We demonstrate that the Earth system's response to the climatic precession, whose amplitude is modulated by the eccentricity with 100-kyr and 400-kyr periodicities, is amplified at the 100-kyr time scale and suppressed at the 400-kyr time scale with the help of the 41-kyr obliquity forcing. Our results also suggest that the present interglacial would not have appeared without the vibrational resonance discovered here.