Autonomous ballooning allows for energy-efficient long-range missions but introduces significant challenges for planning and control algorithms, due to their single degree of actuation: vertical rate control through either buoyancy or vertical thrust. Lateral motion is typically due to the wind; thus, balloon flight is both nonholonomic and often stochastic. Finally, wind is very challenging to sense remotely, and estimates are often available only via low-temporal-and-spatial-frequency predictions from large-scale weather models and direct in situ measurements. In this work, reinforcement learning (RL) is used to generate a control policy for an autonomous balloon navigating between 3D positions in a time- and spatially varying wind field. The agent uses its position and velocity, the relative position of the target, and an estimate of the surrounding wind field to command a target altitude. The wind information contains local measurements and an encoding of global wind predictions from a large-scale numerical weather prediction (NWP) model around the current balloon location. The RL algorithm used in this work, the soft actor-critic (SAC), is trained with a reward favoring paths that reach as close as possible to the target, with minimum time and actuation costs. We evaluate our approach first in simulation and then with a controlled indoor experiment, where we generate an artificial wind field and reach a median distance of 23.4 cm from the target within a volume of 3.5 x 3.5 x 3.5 m over 30 trials. Finally, using a fully autonomous custom designed outdoor prototype capable of controlling altitude, long-range communication, redundant localization, and onboard computation, we validate our approach in a real-world setting. Over six flights, the agent navigates to predefined target positions, with an average target distance error of 360 m after traveling approximately 10 km within a volume of 22 x 22 x 3.2 km.