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 _ { \mathrm { P 1 } } - and i _ { \mathrm { P 1 } } -band imaging data . Both are luminous systems ( M _ { V } \sim - 12 ) located at projected distances of 20.3 ^ { \circ } and 10.5 ^ { \circ } 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 \pm 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 \pm 267 { pc } for Cas III ) , and consequently low surface brightness ( \mu _ { 0 } \sim 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 \pi Pan-STARRS1 survey , which could lead to the discovery of other distant Andromeda satellite dwarf galaxies .