© 2016. The American Astronomical Society. All rights reserved. We present spatially resolved Atacama Large Millimeter/submillimeter Array (ALMA) 870 μm dust continuum maps of six massive, compact, dusty star-forming galaxies at z ∼ 2.5. These galaxies are selected for their small rest-frame optical sizes (reF160W ∼ 1.6 kpc) and high stellar mass densities that suggest that they are direct progenitors of compact quiescent galaxies at z ∼ 2. The deep observations yield high far-infrared (FIR) luminosities of LIR = 1012.3-12.8 L⊙ and star formation rates (SFRs) of SFR = 200-700 M o yr-1, consistent with those of typical star-forming "main sequence" galaxies. The high spatial resolution (FWHM ∼ 0.″12-0.″18) ALMA and Hubble Space Telescope photometry are combined to construct deconvolved, mean radial profiles of their stellar mass and (UV+IR) SFR. We find that the dusty, nuclear IR-SFR overwhelmingly dominates the bolometric SFR up to r ∼ 5 kpc, by a factor of over 100× from the unobscured UV-SFR. Furthermore, the effective radius of the mean SFR profile (re,SFR ∼ 1 kpc) is ∼30% smaller than that of the stellar mass profile. The implied structural evolution, if such nuclear starburst last for the estimated gas depletion time of Δt = ± 100 Myr, is a 4× increase of the stellar mass density within the central 1 kpc and a 1.6× decrease of the half-mass-radius. This structural evolution fully supports dissipation-driven, formation scenarios in which strong nuclear starbursts transform larger, star-forming progenitors into compact quiescent galaxies.