We present new, high angular resolution (~022) MERLIN observations of neutral hydrogen (H I) absorption and λ21 cm radio continuum emission across the central ~900 pc of the ultraluminous infrared galaxy Arp 220. Spatially resolved H I absorption is detected against the morphologically complex and extended λ21 cm radio continuum emission, consistent with two counterrotating disks of neutral hydrogen, with a small bridge of gas connecting the two. Column densities across the two nuclei are high, lying in the range 8 × 10¹⁹T_s(K) N_H 2.4 × 10²⁰T_s(K) cm^-2 (T_s is spin temperature) and corresponding to optical extinctions of 0.052T_s(K) A_V 0.155T_s(K) mag, with the higher column densities in the eastern nucleus. Velocity gradients are clearly visible across each nucleus, reaching 1010 ± 20 km s^-1 kpc^-1 in P.A. ~ 55^° and 830 ± 20 km s^-1 kpc^-1 in P.A. ~ 270^° for eastern and western nuclei, respectively. These gradients imply dynamical masses M_D = 1.1 × 10⁹( i) (E) and 1.7 × 10⁸( i) M (W), assuming that the neutral gas is distributed in two thin circularly rotating disks. We propose a merger model in which the two nuclei represent the galaxy cores that have survived the initial encounter and are now in the final stages of merging, similar to conclusions drawn from previous CO studies. However, we suggest that instead of being coplanar with the main CO disk (in which the eastern nucleus is embedded), the western nucleus lies above it and, as suggested by the bridge of H I connecting the two nuclei, will soon complete its final merger with the main disk. We suggest that the collection of radio supernovae (RSNe) detected in VLBA studies in the more compact western nucleus represents the second burst of star formation associated with this final merger stage and that free-free absorption due to ionized gas in the bulgelike component can account for the observed RSN distribution.