Unmanned aerial vehicles (UAVs) are expected to be an integral part of wireless networks, and determining collision-free trajectories for multiple UAVs while satisfying requirements of connectivity with ground base stations (GBSs) is a challenging task. In this paper, we first reformulate the multi-UAV trajectory optimization problem with collision avoidance and wireless connectivity constraints as a sequential decision making problem in the discrete time domain. We, then, propose a decentralized deep reinforcement learning approach to solve the problem. More specifically, a value network is developed to encode the expected time to destination given the agent's joint state (including the agent's information, the nearby agents' observable information, and the locations of the nearby GBSs). An SINR-prediction network is also designed, using accumulated SINR measurements obtained when interacting with the cellular network, to map the GBSs' locations into the SINR levels in order to predict the UAV's SINR. Numerical results show that with the value network and SINR-prediction network, real-time navigation for multi-UAVs can be efficiently performed in various environments with high success rate.