Binary transition metal fluorides are textbook examples combining complex electronic features with most fundamental molecular structures. High-valent nickel fluorides are among the strongest known fluorinating and oxidizing agents, but there is a lack of experimental structural and spectroscopic investigations on molecular NiF3 or NiF4. Apart from their demanding synthesis, also their quantum-chemical description is difficult due to their open shell nature and low-lying excited electronic states. Distorted tetrahedral NiF4 (D-2d) and trigonal planar NiF3 (D-3h) molecules were produced by thermal evaporation and laser ablation of nickel atoms in a fluorine/noble gas mixture and spectroscopically identified by a joint matrix-isolation and quantum-chemical study. Their vibrational band positions provide detailed insights into their molecular structures.