Automated laser welding with filler wires for bridging gaps and for connecting complex devices has been established for different metal materials. In spite of that, it is still a challenge to transfer this welding process to the brittle material glass. Therefore, glass welding is often realized through a manual process by heating the glass with a gas flame. In addition, welding of non-rotational components requires filler material for gap bridging between the joining partners, which is applied manually today. Thiswork presents an experimental and numerical study on laser welding of fused silica using glass fiber as a filler material to bridge gaps. The goal was to achieve a defined weld penetration depth and heat affected zone which is important for the production of optical elements. Therefore, a CO2 laser heats up the glass components as well as the glass fiber within a temperature controlled welding process. The numerical investigations were used to identify the general process window for welding fused silica. Within the experimental study, the process parameters, such as the defined welding temperature, laser focal spot size, and feed rate were varied to investigate their impact on the welding outcome. In addition, the impact of the filler wire coating on the material composition of the welded component in the joint zone was investigated. Compared to the manual process, laser welding with glass fiber as a filling material leads to a highly reproducible process enabling a high automation level.