One of the key challenges in robotic remote laser 3D processing (RL3DP) is to achieve high accuracy for the laser’s working trajectory relative to the features of the workpiece. This paper presents a novel RL3DP system with an automatic 3D teaching functionality for a precise and rapid determination of the working trajectory which comprises a robot manipulator, 3D scanning head, fibre laser and an off-axis positioned camera. The 3D measurement is based on laser triangulation with laser-stripe illumination using the laser’s pilot beam and scanning head. The experimental results show that the system has a precision better than 70 µm and 120 µm along lateral and vertical direction respectively inside the measuring range of 100 × 100 mm. The teaching time is 30-times shorter compared to a visual teaching procedure. Therefore, such a system can lead to large cost reductions for modern production lines that have constant changes to the products’ geometries and functionalities.