We present stellar mass surface density profiles of a mass-selected sample of 177 galaxies at 0.5 < z < 2.5, obtained using very deep HST optical and near-infrared data over the GOODS-South field, including recent CANDELS data. Accurate stellar mass surface density profiles have been measured for the first time for a complete sample of high-redshift galaxies more massive than 10^10.7 M_sun. The key advantage of this study compared to previous work is that the surface brightness profiles are deconvolved for PSF smoothing, allowing accurate measurements of the structure of the galaxies. The surface brightness profiles account for contributions from complex galaxy structures such as rings and faint outer disks. Mass profiles are derived using radial rest-frame u-g color profiles and a well-established empirical relation between these colors and the stellar mass-to-light ratio. We derive stellar half-mass radii from the mass profiles, and find that these are on average ~25% smaller than rest-frame g band half-light radii. This average size difference of 25% is the same at all redshifts, and does not correlate with stellar mass, specific star formation rate, effective surface density, Sersic index, or galaxy size. Although on average the difference between half-mass size and half-light size is modest, for approximately 10% of massive galaxies this difference is more than a factor two. These extreme galaxies are mostly extended, disk-like systems with large central bulges. These results are robust, but could be impacted if the central dust extinction becomes high. ALMA observations can be used to explore this possibility. These results provide added support for galaxy growth scenarios wherein massive galaxies at these epochs grow by accretion onto their outer regions.