We present specific star formation rate (sSFR) radial profiles for a sample of 161 relatively face-on spiral galaxies from the GALEX Atlas of Nearby Galaxies. The sSFR profiles are derived from GALEX and 2MASS (FUV - K) color profiles after a proper SFR calibration of the UV luminosity and K-band mass-to-light ratio are adopted. The (FUV - K) profiles were first corrected for foreground Galactic extinction and later for internal extinction using the ratio of the total-infrared (TIR) to FUV emission. For those objects where TIR-to-FUV ratio radial profiles were not available, the (FUV - NUV) color profiles were used as a measure of the UV slope. The sSFR radial gradients derived from these profiles allow us to quantify the inside-out scenario for the growth of spiral disks for the first time in the local universe. We find a large dispersion in the slope of the sSFR profiles with a slightly positive mean value, which implies a moderate inside-out disk formation. There is also a strong dependency of the value of this slope on the luminosity and size of the disks, with large systems showing a uniform, slightly positive slope in almost all cases and low-luminosity small disks showing a large dispersion with both positive and negative large values. While a majority of the galaxies can be interpreted as forming stars gradually either from inside out or from outside in, a few disks require episodes of enhanced recent growth with scale lengths of the SFR (or gas infall) being significantly larger at present than in the past. We do not find any clear dependence of the sSFR gradient on the environment (local galaxy density or presence of close neighbors).