The fabrication of optoelectronic devices such as light-emitting diodes (LEDs) typically involves photolithography steps, requiring specific lithography masks. This approach is expensive, inflexible and time consuming, in particular for prototyping. Therefore it would be attractive to replace these steps by direct writing techniques such as laser processing, which would speed up, for example the development and prototyping of new devices. Picosecond lasers provide a universal tool for material processing. Due to the short pulse length, material is removed by a process called "cold ablation," with minimal thermal damage to neighboring regions. As a result, better-defined structures with smoother and cleaner side walls can be fabricated compared to nanosecond-pulsed laser-based processing. We report on fully laser-processed planar gallium nitride-based LEDs fabricated using only ps laser processing for pattern definition and material removal. On the bare semiconductor wafer, isolation trenches and mesa structures are formed directly by ultraviolet ps laser pulse writing. For the direct deposition of patterned ohmic contact metallizations, the ps laser fabrication and subsequent use of high-resolution shadow masks is presented. Finally, the ps laser-processed LEDs are electrically and optically characterized and their characteristics compared with those of conventionally fabricated mesa LEDs.