Most works on cell-free massive multiple-input multiple-output (MIMO) consider non-cooperative precoding strategies at the base stations (BSs) to avoid extensive channel state information (CSI) exchange via backhaul signaling. However, considerable performance gains can be accomplished by allowing coordination among the BSs. This paper proposes the first distributed framework for cooperative precoding design in cell-free massive MIMO (and, more generally, in joint transmission coordinated multi-point) systems that entirely eliminates the need for backhaul signaling for CSI exchange. A novel over-the-air (OTA) signaling mechanism is introduced such that each BS can obtain the same cross-term information that is traditionally exchanged among the BSs via backhaul signaling. The proposed distributed precoding design enjoys desirable flexibility and scalability properties, as the amount of OTA signaling does not scale with the number of BSs or user equipments. Numerical results show fast convergence and remarkable performance gains as compared with non-cooperative precoding design. The proposed scheme can also outperform the centralized precoding design under realistic CSI acquisition.