  The recent discoveries of WD J091405.30+191412.25 (WD J0914 hereafter), a
white dwarf likely accreting material from an ice giant planet, and WD 1856+534
b (WD 1856 b hereafter), a Jupiter-sized planet transiting a white dwarf, are
the first direct evidence of giant planets orbiting white dwarfs. However, for
both systems the observations indicate that the planets' current orbital
distances would have put them inside the stellar envelope during the red giant
phase, implying that the planets must have migrated to their current orbits
after their host stars became white dwarfs. Furthermore, WD J0914 is a very hot
white dwarf with a short cooling time that indicates a fast migration
mechanism. Here, we demonstrate that the Eccentric Kozai-Lidov (EKL) Mechanism,
combined with stellar evolution and tidal effects, can naturally produce the
observed orbital configurations, assuming that the white dwarfs have distant
stellar companions. Indeed, WD 1856 is part of a stellar triple system, being a
distant companion to a stellar binary. We provide constraints for the orbital
and physical characteristics for the potential stellar companion of WD J0914
and determine the initial orbital parameters of the WD 1856 system.
