In this paper we provide empirical evidence that using humanlike gaze cues during human-robot handovers can improve the timing and perceived quality of the handover event. Handovers serve as the foundation of many human-robot tasks. Fluent, legible handover interactions require appropriate nonverbal cues to signal handover intent, location and timing. Inspired by observations of human-human handovers, we implemented gaze behaviors on a PR2 humanoid robot. The robot handed over water bottles to a total of 102 naïve subjects while varying its gaze behaviour: no gaze, gaze designed to elicit shared attention at the handover location, and the shared attention gaze complemented with a turn-taking cue. We compared subject perception of and reaction time to the robot-initiated handovers across the three gaze conditions. Results indicate that subjects reach for the offered object significantly earlier when a robot provides a shared attention gaze cue during a handover. We also observed a statistical trend of subjects preferring handovers with turn-taking gaze cues over the other conditions. Our work demonstrates that gaze can play a key role in improving user experience of human-robot handovers, and help make handovers fast and fluent.