We present HST/WFPC2 observations of the five bluest E+A galaxies (z~0.1) in the Zabludoff et al. sample to study whether their detailed morphologies are consistent with late-to-early type evolution and to determine what drives that evolution. The morphologies of four galaxies are disturbed, indicating that a galaxy-galaxy merger is at least one mechanism that leads to the E+A phase. Two-dimensional image fitting shows that the E+As are generally bulge-dominated systems, even though at least two E+As may have underlying disks. In the Fundamental Plane, E+As stand apart from the E/S0s mainly due to their high effective surface brightness. Fading of the young stellar population and the corresponding increase in their effective radii will cause these galaxies to migrate toward the locus of E/S0s. E+As have profiles qualitatively like those of normal power-law early-type galaxies, but have higher surface brightnesses. This result provides the first direct evidence supporting the hypothesis that power-law ellipticals form via gas-rich mergers. In total, at least four E+As are morphologically consistent with early-type galaxies. We detect compact sources, possibly young star clusters, associated with the galaxies. These sources are much brighter (M_R ~ -13) than Galactic globular clusters, have luminosities consistent with the brightest clusters in nearby starburst galaxies, and have blue colors consistent with the ages estimated from the E+A galaxy spectra (several 10^8 yr). Further study of such young star cluster candidates might provide the elusive chronometer needed to break the age/burst-strength degeneracy for these post-merger galaxies.

30 pages, 11 figures, accepted for publication in ApJ