Object handover is the fundamental collaborative action requiring robots and humans to physically interact. When the robotic partner plays the giver role, it assumes the responsibility of safely and fluently conducting the handover, aiming to enhance the quality of the action perceived by the human receiver. In these terms, complex scenarios, such as conditions for which the robot must reach the partner to present the object to handover, really pose the challenge of preserving good coordination concerning the observed intention of the human. A crucial aspect is gaining the correct timing for the beginning of the object release and regulating its duration. Here we show that robot proprioception and observation of the human partner kinematics are key aspects to successfully deal with these issues. We present a handover control policy based on two modules. The first consists of a filtering technique which guarantees the correct reactivity of the robot by estimating and interpreting the interaction forces generated during the handover. The second module is a bio-inspired control law for the object release, aiming for the best possible coordination with the human partner. The control policy has been implemented in a robot arm equipped with a sensorised artificial hand and assessed by 15 participants asked to hand over a test object using different reaching dynamics. The control policy proved to be reliable since we did not record failures of the handover in 180 trials, and coordinated to the handover dynamics of the receiver, although it did not outperform fast feed-forward releases.