We present multi-epoch, high-dispersion, optical spectra obtained with the Michigan/Magellan Fiber System of 126 and 125 Sun-like stars in the young clusters NGC 2516 (141Myr) and NGC 2422 (73Myr). We determine stellar properties including radial velocity (RV), Teff, [Fe/H], [{alpha}/Fe], and the line-of-sight rotation rate, v_r_sin(i), from these spectra. Our median RV precision of 80m/s on individual epochs that span a temporal baseline of 1.1yr enables us to investigate membership, stellar binarity, and search for sub-stellar companions. We determine membership probabilities and RV variability probabilities for our sample along with candidate companion orbital periods for a select subset of stars. We identify 81 RV members in NGC 2516, 27 spectroscopic binaries (17 previously identified as photometric binaries), and 16 other stars that show significant RV variability after accounting for average stellar jitter found to be at the 74m/s level. In NGC 2422 we identify 57 members, 11 spectroscopic binaries, and 3 other stars that show significant RV variability after accounting for an average jitter of 138m/s. We use Monte Carlo simulations to verify our stellar jitter measurements, determine the proportion of exoplanets and stellar companions to which we are sensitive, and estimate companion mass limits for our targets. We also report mean cluster metallicity, velocity, and velocity dispersion based on our member targets and identify 58 non-member stars as RV variables - 24 of which have RV amplitudes that imply stellar or brown-dwarf mass companions. Finally, we note the discovery of a separate RV clustering of stars in our NGC 2422 sample.