During voluntary hand movement, we sense that we generate the movement and that the hand is a part of our body. These feelings of control over bodily actions, or the sense of agency, and the ownership of body parts are two fundamental aspects of the way we consciously experience our bodies. However, little is known about how these processes are functionally linked. Here, we introduce a version of the rubber hand illusion in which participants control the movements of the index finger of a model hand, which is in full view, by moving their own right index finger. We demonstrated that voluntary finger movements elicit a robust illusion of owning the rubber hand and that the senses of ownership and agency over the model hand can be dissociated. We systematically varied the relative timing of the finger movements (synchronous versus asynchronous), the mode of movement (active versus passive), and the position of the model hand (anatomically congruent versus incongruent positions). Importantly, asynchrony eliminated both ownership and agency, passive movements abolished the sense of agency but left ownership intact, and incongruent positioning of the model hand diminished ownership but did not eliminate agency. These findings provide evidence for a double dissociation of ownership and agency, suggesting that they represent distinct cognitive processes. Interestingly, we also noted that the sense of agency was stronger when the hand was perceived to be a part of the body, and only in this condition did we observe a significant correlation between the subjects’ ratings of agency and ownership. We discuss this in the context of possible differences between agency over owned body parts and agency over actions that involve interactions with external objects. In summary, the results obtained in this study using a simple moving rubber hand illusion paradigm extend previous findings on the experience of ownership and agency and shed new light on their relationship.