Cell-free massive multiple-input multiple-output (MIMO) is a promising cellular network. In this network, a large number of distributed and multi-antenna access points (APs) jointly serve many single antenna users using the same time-frequency resource. Consequently, it possibly provides a uniform service experience to users regardless of the users' locations by eliminating interference at cell boundaries via user-centric joint transmission. This joint transmission, however, requires extremely high signaling overheads for data sharing via backhaul links and causes a high network-wide power consumption. To resolve these problems, in this paper, we present a novel joint transmission method, which is referred to as sparse joint transmission (sparse-JT), for cell-free massive MIMO networks with finite backhaul capacity constraints. Sparse-JT jointly identifies the user-centric cooperative APs sets, precoding vectors for beamforming and compression, and power allocation that maximizes a lower bound of the sum-spectral efficiency under the constraint that a total number of active APs per the joint transmission is sparse. The proposed algorithm guarantees to identify a local-optimal solution for a relaxed sum-spectral maximization problem. By simulations, we show that sparse-JT achieves higher ergodic spectral efficiencies than those attained by multi-cell zero-forcing precoding with the user-centric AP clustering algorithm in all system configurations.