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Abstract From >1000 orbits of HST imaging, we present deep homogeneous resolved star color–magnitude diagrams that reach the oldest main-sequence turnoff and uniformly measured star formation histories (SFHs) of 36 dwarf galaxies (−6 ≥M_V≥ −17) associated with the M31 halo, and for 10 additional fields in M31, M33, and the Giant Stellar Stream. From our SFHs, we find: (i) The median stellar age and quenching epoch of M31 satellites correlate with galaxy luminosity and galactocentric distance. Satellite luminosity and present-day distance from M31 predict the satellite quenching epoch to within 1.8 Gyr at all epochs. This tight relationship highlights the fundamental connection between satellite halo mass, environmental history, and star formation duration. (ii) There is no difference between the median SFH of galaxies on and off the great plane of Andromeda satellites. (iii) ~50% of our M31 satellites show prominent ancient star formation (>12 Gyr ago) followed by delayed quenching (8–10 Gyr ago), which is not commonly observed among the MW satellites. (iv) A comparison with TNG50 and FIRE-2 simulated satellite dwarfs around M31-like hosts shows that some of these trends (dependence of SFH on satellite luminosity) are reproduced in the simulations while others (dependence of SFH on galactocentric distance, presence of the delayed-quenching population) are weaker or absent. We provide all photometric catalogs and SFHs as High-Level Science Products on MAST.