We study the growth of massive galaxies from z=2 to the present using data from the NEWFIRM Medium Band Survey. The sample is selected at a constant number density of n=2x10^-4 Mpc^-3, so that galaxies at different epochs can be compared in a meaningful way. We show that the stellar mass of galaxies at this number density has increased by a factor of ~2 since z=2, following the relation log(M)=11.45-0.15z. In order to determine at what physical radii this mass growth occurred we construct very deep stacked rest-frame R-band images at redshifts z=0.6, 1.1, 1.6, and 2.0. These image stacks of typically 70-80 galaxies enable us to characterize the stellar distribution to surface brightness limits of ~28.5 mag/arcsec^2. We find that massive galaxies gradually built up their outer regions over the past 10 Gyr. The mass within a radius of r=5 kpc is nearly constant with redshift whereas the mass at 5-75 kpc has increased by a factor of ~4 since z=2. Parameterizing the surface brightness profiles we find that the effective radius and Sersic n parameter evolve as r_e~(1+z)^-1.3 and n~(1+z)^-1.0 respectively. The data demonstrate that massive galaxies have grown mostly inside-out, assembling their extended stellar halos around compact, dense cores with possibly exponential radial density distributions. Comparing the observed mass evolution to the average star formation rates of the galaxies we find that the growth is likely dominated by mergers, as in-situ star formation can only account for ~20% of the mass build-up from z=2 to z=0. The main uncertainties in this study are possible redshift-dependent systematic errors in the total stellar masses and the conversion from light-weighted to mass-weighted radial profiles.
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