The ability to manipulate the multiple properties of light diversifies light-matter interaction and light-driven applications. Here, using quantum control, we introduce an approach that enables the amplitude, sign, and even configuration of the generated light fields to be manipulated in an all-optical manner. Following this approach, we demonstrate the generation of "flying doughnut" terahertz (THz) pulses. We show that the single-cycle THz pulse radiated from the dynamic ring current has an electric field structure that is azimuthally polarized and that the space- and time-resolved magnetic field has a strong, isolated longitudinal component. We apply the flying doughnut pulse for a spectroscopic measurement of the water vapor in ambient air. Pulses such as these will serve as unique probes for spectroscopy, imaging, telecommunications, and magnetic materials.