We present deep Magellan+Megacam imaging of Centaurus I (Cen I) and Eridanus IV (Eri IV), two recently discovered Milky Way ultrafaint satellites. Our data reach similar to 2-3 mag deeper than the discovery data from the DECam Local Volume Exploration Survey. We use these data to constrain their distances, structural properties (e.g., half-light radii, ellipticity, and position angle), and luminosities. We investigate whether these systems show signs of tidal disturbance and identify new potential member stars using Gaia EDR3. Our deep color-magnitude diagrams show that Cen I and Eri IV are consistent with an old (tau similar to 13.0 Gyr) and metal-poor ([Fe/H] <= -2.2) stellar population. We find Cen I to have a half-light radius of r(h)=2.' 60 +/- 0.' 30(90.6 +/- 11 pc), an ellipticity of = 0.36 +/- 0.05, a distance of D = 119.8 +/- 4.1 kpc (m - M = 20.39 +/- 0.08 mag), and an absolute magnitude of M-V = -5.39 +/- 0.19. Similarly, Eri IV has r(h)=3.' 24 +/- 0.' 48(65.9 +/- 10 pc), = 0.26 +/- 0.09, D = 69.9 +/- 3.6 kpc (m - M = 19.22 +/- 0.11 mag), and M-V = -3.55 +/- 0.24. These systems occupy a space on the size-luminosity plane consistent with other known Milky Way dwarf galaxies, which supports the findings from our previous spectroscopic follow-up. Cen I has a well-defined morphology that lacks any clear evidence of tidal disruption, whereas Eri IV hosts a significant extended feature with multiple possible interpretations.