We present results of a statistical study of the cosmic evolution of the mass-dependent major-merger rate since z = 1. A stellar mass limited sample of close major-merger pairs (the CPAIR sample) was selected from the archive of the COSMOS survey. Pair fractions at different redshifts derived using the CPAIR sample and a local K-band-selected pair sample show no significant variations with stellar mass. The pair fraction exhibits moderately strong cosmic evolution, with the best-fitting function of functionof sub(pair) = 10 super(-1.88(+ or - 0.03))(1 + z) super(2.2(+ or - 0.2)). The best-fitting function for the merger rate is R sub(mg) (Gyr super(-1)) = 0.053 x (M sub(star)/10 super(10.7) M sub(middot in circle)) super(0.3)(1 + z) super(2.2)/(1 + z/8). This rate implies that galaxies of M sub(star) ~ 10 super(10)-10 super(11.5) M sub(middot in circle) have undergone ~0.5-1.5 major mergers since z = 1. Our results show that, for massive galaxies (M sub(star) > or =, slanted 10 super(10.5) M sub(middot in circle)) at z < or =, slant 1, major mergers involving star-forming galaxies (i.e., wet and mixed mergers) can account for the formation of both ellipticals and red quiescent galaxies (RQGs). On the other hand, major mergers cannot be responsible for the formation of most low mass ellipticals and RQGs of M sub(star) <, ~ 10 super(10.3) M sub(middot in circle). Our quantitative estimates indicate that major mergers have significant impact on the stellar mass assembly of the most massive galaxies (M sub(star) > or =, slanted 10 super(11.3) M sub(middot in circle)), but for less massive galaxies the stellar mass assembly is dominated by the star formation. Comparison with the mass-dependent (ultra)luminous infrared galaxies ((U)LIRG) rates suggests that the frequency of major-merger events is comparable to or higher than that of (U)LIRGs.