The fullerene C$_{60}$ has four infrared-active vibrational transitions at 7.0, 8.5, 17.4 and 18.9 $mu$m. We have previously observed emission features at 17.4 and 18.9 $mu$m in the reflection nebula NGC 7023 and demonstrated spatial correlations suggestive of a common origin. We now confirm our earlier identification of these features with C$_{60}$ by detecting a third emission feature at 7.04 $pm$ 0.05 $mu$m in NGC 7023. We also report the detection of these three C$_{60}$ features in the reflection nebula NGC 2023. Our spectroscopic mapping of NGC 7023 shows that the 18.9 $mu$m C$_{60}$ feature peaks on the central star and that the 16.4 $mu$m emission feature due to polycyclic aromatic hydrocarbons peaks between the star and a nearby photodissociation front. The observed features in NGC 7023 are consistent with emission from UV-excited gas-phase C$_{60}$. We find that 0.1-0.6% of interstellar carbon is in C$_{60}$; this abundance is consistent with those from previous upper limits and possible fullerene detections in the interstellar medium. This is the first firm detection of neutral C$_{60}$ in the interstellar medium.