Exploiting the power of gravitational lensing, the Hubble Frontier Fields (HFF) program aims at observing six massive galaxy clusters to explore the distant universe far beyond the limits of blank field surveys. Using the complete Hubble Space Telescope observations of the first HFF cluster A2744, we report the detection of 50 galaxy candidates at z similar to 7 and eight candidates at z similar to 8 in a total survey area of 0.96 arcmin(2) in the source plane. Three of these galaxies are multiply imaged by the lensing cluster. Using an updated model of the mass distribution in the cluster we were able to calculate the magnification factor and the effective survey volume for each galaxy in order to compute the ultraviolet galaxy luminosity function (LF) at both redshifts 7 and 8. Our new measurements reliably extend the z similar to 7 UV LF down to an absolute magnitude of M-UV similar to -15.5. We find a characteristic magnitude of M-UV* = -20.90(0.73)(+0.90) mag and a faint-end slope alpha = -2.01(-0.28)(+0.20), close to previous determinations in blank fields. We show here for the first time that this slope remains steep down to very faint luminosities of 0.01 L*. Although prone to large uncertainties, our results at z similar to 8 also seem to confirm a steep faint- end slope below 0.1 L*. The HFF program is therefore providing an extremely efficient way to study the faintest galaxy populations at z > 7 that would otherwise be inaccessible with current instrumentation. The full sample of six galaxy clusters will provide even better constraints on the buildup of galaxies at early epochs and their contribution to cosmic reionization.