The EU-funded project BASTA (Boost Applied munition detection through Smart data inTegration and AI workflows, http://www.basta-munition.eu) aimed at improving underwater unexploded ordnance (UXO) detection approaches and advancing data acquisition techniques. One aspect of the project was performing autonomous underwater vehicle (AUV)-based magnetic measurements. In this paper, we present the first results of integrating three submersible fluxgate magnetometers to a Girona 500 AUV in the context of underwater UXO detection. The hovering capabilities of these AUVs allow them to maintain a fixed position or to precisely navigate at very low velocities and altitudes. The magnetic sensors are rigidly attached to the nose of the AUV at a lateral distance of 2 m and are arranged in the shape of a vertical triangle, thereby allowing for the calculation of three spatial magnetic gradients. A series of surveys was performed when visiting several munitions dumpsites in the German Baltic Sea. Furthermore, we successfully conducted a test survey with surrogate objects of known magnetic moments in a naval port basin in Kiel, Germany. With a noise floor of approximately 2 nT, the system is capable of reliably detecting munitions similar in size to 81 mm shells from altitudes of 1 m above the seafloor. For ground-truthing purposes and for a concluding confirmation or rejection of a UXO suspicion, the AUV is equipped with a high-resolution camera system. This newly developed system aims at improving the industry standard's technical potentials of autonomously discriminating between hazardous UXO and anthropogenic debris or rocks and therefore reducing the number of target points before underwater UXO clearance campaigns.