© 2019. The American Astronomical Society. All rights reserved.. Supernovae that are strongly gravitationally lensed (gLSNe) by elliptical galaxies are powerful probes of astrophysics and cosmology that will be discovered systematically by wide-field, high-cadence imaging surveys such as the Zwicky Transient Facility (ZTF) and the Large Synoptic Survey Telescope (LSST). Here we use pixel-level simulations that include observing strategy, target selection, supernova properties, and dust to forecast the rates and properties of gLSNe that ZTF and LSST will find. Applying the resolution-insensitive discovery strategy of Goldstein et al., we forecast that ZTF (LSST) can discover 0.02 (0.79) 91bg-like, 0.17 (5.92) 91T-like, 1.22 (47.84) Type Ia, 2.76 (88.51) Type IIP, 0.31 (12.78) Type IIL, and 0.36 (15.43) Type Ib/c gLSNe per year, with uncertainties dominated by uncertainties in the supernova rate. We also forecast that the surveys can discover at least 3.75 (209.32) Type IIn gLSNe per year, for a total of at least 8.60 (380.60) gLSNe per year under fiducial observing strategies. ZTF gLSNe have a median z s = 0.9, z l = 0.35, , Δt max = 10 days, min(θ) = 0.″25, and N img = 4. LSST gLSNe are less compact and less magnified, with a median z s = 1.0, z l = 0.4, , Δt max = 25 days, min(θ) = 0.″6, and N img = 2. We develop a model of the supernova-host galaxy connection and find that the vast majority of gLSN host galaxies will be multiply imaged, enabling detailed constraints on lens models with sufficiently deep high-resolution imaging taken after the supernova has faded. We release the results of our simulations as catalogs at http://portal.nersc.gov/project/astro250/glsne/.