© 2021. The American Astronomical Society. All rights reserved. We used existing data from the New Horizons Long-range Reconnaissance Imager (LORRI) to measure the optical-band (0.4 ≲ λ ≲ 0.9 μm) sky brightness within seven high-Galactic latitude fields. The average raw level measured while New Horizons was 42-45 au from the Sun is 33.2 ± 0.5 nW m−2 sr−1. This is ∼10× as dark as the darkest sky accessible to the Hubble Space Telescope, highlighting the utility of New Horizons for detecting the cosmic optical background (COB). Isolating the COB contribution to the raw total required subtracting scattered light from bright stars and galaxies, faint stars below the photometric detection limit within the fields, and diffuse Milky Way light scattered by infrared cirrus. We removed newly identified residual zodiacal light from the IRIS 100 μm all-sky maps to generate two different estimates for the diffuse Galactic light. Using these yielded a highly significant detection of the COB in the range 15.9 ± 4.2 (1.8 stat., 3.7 sys.) nW m−2 sr−1 to 18.7 ± 3.8 (1.8 stat., 3.3 sys.) nW m−2 sr−1 at the LORRI pivot wavelength of 0.608 μm. Subtraction of the integrated light of galaxies fainter than the photometric detection limit from the total COB level left a diffuse flux component of unknown origin in the range 8.8 ± 4.9 (1.8 stat., 4.5 sys.) nW m−2 sr−1 to 11.9 ± 4.6 (1.8 stat., 4.2 sys.) nW m−2 sr−1. Explaining it with undetected galaxies requires the assumption that the galaxy count faint-end slope steepens markedly at V > 24 or that existing surveys are missing half the galaxies with V < 30.