We report the discovery of two new dwarf galaxies, Lacerta I/Andromeda XXXI (Lac I/And XXXI) and Cassiopeia III/Andromeda XXXII (Cas III/And XXXII), in stacked Pan-STARRS1 r_P1- and i_P1-band imaging data. Both are luminous systems (M_V ~ -12) located at projected distances of 20.3{\deg} and 10.5{\deg} from M31. Lac I and Cas III are likely satellites of the Andromeda galaxy with heliocentric distances of 756^{+44}_{-28} kpc and 772^{+61}_{-56} kpc, respectively, and corresponding M31-centric distances of 275+/-7 kpc and 144^{+6}_{-4} kpc . The brightest of recent Local Group member discoveries, these two new dwarf galaxies owe their late discovery to their large sizes (r_h = 4.2^{+0.4}_{-0.5} arcmin or 912^{+124}_{-93} pc for Lac I; r_h = 6.5^{+1.2}_{-1.0} arcmin or 1456+/-267 pc for Cas III), and consequently low surface brightness (μ_0 ~ 26.0 mag/arcsec^2), as well as to the lack of a systematic survey of regions at large radii from M31, close to the Galactic plane. This latter limitation is now alleviated by the 3{π} Pan-STARRS1 survey, which could lead to the discovery of other distant Andromeda satellite dwarf galaxies. ; Comment: 7 pages, 5 figures. Accepted for publication in ApJ