We present the results of a set of numerical simulations of long-duration gamma-ray burst jets associated with massive, compact stellar progenitors. The simulations extend to large radii and allow us to locate the region in which the peak frequency of the advected radiation is set before the radiation is released at the photosphere. Light curves and spectra are calculated for different viewing angles as well as different progenitor structures and jet properties. We find that the radiation released at the photosphere of matter-dominated jets is able to reproduce the observed Amati and energy-Lorentz factor correlations. Our simulations also predict a correlation between the burst energy and the radiative efficiency of the prompt phase, consistent with observations.