We used the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) near-infrared camera to image the host galaxies of a sample of 11 luminous, dust-reddened quasars at z ∼ 2—the peak epoch of black hole growth and star formation in the universe—to test the merger-driven picture for the coevolution of galaxies and their nuclear black holes. The red quasars come from the FIRST+2MASS red quasar survey and a newer, deeper, UKIDSS +FIRST sample. These dust-reddened quasars are the most intrinsically luminous quasars in the universe at all redshifts, and they may represent the dust-clearing transitional phase in the merger-driven black hole growth scenario. Probing the host galaxies in rest-frame visible light, the HST images reveal that 8/10 of these quasars have actively merging hosts, whereas one source is reddened by an intervening lower-redshift galaxy along the line of sight. We study the morphological properties of the quasar hosts using parametric Sérsic fits, as well as nonparametric estimators (Gini coefficient, M20, and asymmetry). Their properties are heterogeneous but broadly consistent with the most extreme morphologies of local merging systems such as ultraluminous infrared galaxies. The red quasars have a luminosity range of log( ) 47.8 48.3 Lbol = − (erg s−1 ), and the merger fraction of their hosts is consistent with merger-driven models of luminous active galactic nuclei activity at z = 2, which supports the picture in which luminous quasars and galaxies coevolve through major mergers that trigger both star formation and black hole growth.