Relativistic outflows in the form of jets are common in many astrophysical objects. By their very nature, jets have angle dependent velocity profiles, Gamma = Gamma(r, theta, phi), where Gamma is the outflow Lorentz factor. In this work we consider photospheric emission from non-dissipative jets with various Lorentz factor profiles, of the approximate form Gamma \approx Gamma_0/[(theta/theta_j)^p + 1], were theta_j is the characteristic jet opening angle. In collimated jets, the observed spectrum depends on the viewing angle, theta_v. We show that for narrow jets (theta_j Gamma_0 \lesssim few), the obtained low energy photon index is alpha \approx -1 (dN/dE \propto E^alpha), independent of viewing angle, and weakly dependent on the Lorentz factor gradient (p). A similar result is obtained for wider jets observed at theta_v \approx theta_j. This result is surprisingly similar to the average low energy photon index seen in gamma-ray bursts. For wide jets (theta_j Gamma_0 \gtrsim few) observed at theta_v \ll theta_j, a multicolor blackbody spectrum is obtained. We discuss the consequences of this theory on our understanding of the prompt emission in gamma-ray bursts.