We present follow-up spectroscopy of the galaxy cluster MS1054-03 (z=0.83) confirming that at least six of the nine merging galaxy pairs identified by van Dokkum et al. (1999) are indeed bound systems: they have projected separations of R_s<10 kpc and relative line-of sight velocities of dv<165 km/s. For the remaining three pairs, we were unable to obtain redshifts of both constituent galaxies. To identify a more objective sample of merging systems, we select bound red galaxy pairs (R_s<=30 kpc, dv<=300 km/s) from our sample of 121 confirmed cluster members: galaxies in bound red pairs make up 15.7+/-3.6% of the cluster population. The (B-K_s) color-magnitude diagram shows that the pair galaxies are as red as the E/S0 members and have a homogeneous stellar population. The red pair galaxies span a large range in luminosity and internal velocity dispersion to include some of the brightest, most massive members (L>L*, sigma>200 km/s); these bound galaxy pairs must evolve into E/S0 members by z~0.7. These results combined with MS1054's high merger fraction and reservoir of likely future mergers indicates that most, if not all, of its early-type members evolved from (passive) galaxy-galaxy mergers at z<~1.