The problem of safe planning and control for multi- drone systems across a variety of missions is of critical importance, as the scope of tasks assigned to such systems increases. In this paper, we present an approach to solve this problem for multi-quadrotor missions. Given a mission expressed in Signal Temporal Logic (STL), our controller maximizes robustness to generate trajectories for the quadrotors that satisfy the STL specification in continuous-time. We also show that the constraints on our optimization guarantees that these trajectories can be tracked nearly perfectly by lower level off-the-shelf position and attitude controllers. Our approach avoids the oversimplifying abstractions found in many planning methods, while retaining the expressiveness of missions encoded in STL allowing us to handle complex spatial, temporal and reactive requirements. Through experiments, both in simulation and on actual quadrotors, we show the performance, scalability and real-time applicability of our method.