We report the detection, with a high level of confidence, of coherent outflows around voids found in the seventh data release of the Sloan Digital Sky Survey (SDSS DR7). In particular, we developed a robust ⟨|cos θ|⟩ statistical test to quantify the strength of redshift-space distortions (RSD) associated with extended coherent velocity fields. We consistently find that the vector that joins void centers with galaxies that lie in shells around them is more likely to be perpendicular to the line-of-sight than parallel to it. This effect is clear evidence for the existence of outflows in the vicinity of voids. We show that the RSD exist for a wide range of void radius and shell thickness, but they are more evident in the largest voids in our sample. For instance, we find that the ⟨|cos θ|⟩ for galaxies located in shells within 2 h-1Mpc from the edge of voids larger than 15 h-1Mpc deviates 3.81σ from uniformity. The measurements presented in this work provide useful information to constrain cosmological parameters, in particular Ωm and σ8.