We analyze the morphological properties of a large sample of 1503 70 micron selected galaxies in the COSMOS field spanning the redshift range 0.01<z< 3.5 with a median redshift of 0.5 and an infrared luminosity range of 10^8<L_IR<10^14L_sun with a median luminosity of 10^11.4 L_sun. In general these galaxies are massive, with a stellar mass range of 10^10-10^12 M_sun, and luminous, with -25<M_K<-20. We find a strong correlation between the fraction of major mergers and L_IR, with the fraction at the highest luminosity being up to 50%. We also find that the fraction of spirals drops dramatically with L_IR. Minor mergers likely play a role in boosting the infrared luminosity for sources with low luminosities. The precise fraction of mergers in any given L_IR bin varies by redshift due to sources at z>1 being difficult to classify and subject to the effects of band pass shifting, therefore, these numbers can only be considered lower limits. At z<1, where the morphological classifications are most robust, major mergers clearly dominate the ULIRG population (50-80%) and are important for the LIRG population (25-40%). At z>1 the fraction of major mergers is at least 30-40% for ULIRGs. Although the general morphological trends agree with what has been observed for local (U)LIRGs, the fraction of major mergers is slightly lower than seen locally. This is in part due to the difficulty of identifying merger signatures at high redshift. We argue that given the number of major gas-rich mergers observed and the relatively short timescale that they would be observable in the (U)LIRG phase that it is plausible for the observed red sequence of massive ellipticals (<10^12 M_sun) to have been formed entirely by gas-rich major mergers.
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