Low-loss nanostructured dielectric metasurfaces have emerged as a breakthrough platform for ultrathin optics and cutting-edge photonic applications, including beam shaping, focusing, and holography. However, the static nature of their constituent materials has traditionally limited them to fixed functionalities. Tunable all-dielectric infrared Huygens' metasurfaces consisting of multi-layer Ge disk meta-units with strategically incorporated non-volatile phase change material Ge3Sb2Te6 are introduced. Switching the phase-change material between its amorphous and crystalline structural state enables nearly full dynamic light phase control with high transmittance in the mid-IR spectrum. The metasurface is realized experimentally, showing post-fabrication tuning of the light phase within a range of 81% of the full 2 pi phase shift. Additionally, the versatility of the tunable Huygen's metasurfaces is demonstrated by optically programming the spatial light phase distribution of the metasurface with single meta-unit precision and retrieving high-resolution phase-encoded images using hyperspectral measurements. The programmable metasurface concept overcomes the static limitations of previous dielectric metasurfaces, paving the way for "universal" metasurfaces and highly efficient, ultracompact active optical elements like tunable lenses, dynamic holograms, and spatial light modulators.