We used existing data from the New Horizons LORRI camera to measure the optical-band ($0.4lesssimlambdalesssim0.9{rmmu m}$) sky brightness within seven high galactic latitude fields. The average raw level measured while New Horizons was 42 to 45 AU from the Sun is $33.2pm0.5{rm ~nW ~m^{-2} ~sr^{-1}}.$ This is $sim10times$ darker than the darkest sky accessible to the {it Hubble Space Telescope}, highlighting the utility of New Horizons for detecting the cosmic optical background (COB). Isolating the COB contribution to the raw total requires 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 remove newly identified residual zodiacal light from the IRIS $100mu$m all sky maps to generate two different estimates for the diffuse galactic light (DGL). Using these yields a highly significant detection of the COB in the range ${rm 15.9pm 4.2 (1.8~stat., 3.7~sys.) ~nW ~m^{-2} ~sr^{-1}}$ to ${rm 18.7pm 3.8 (1.8~stat., 3.3 ~sys.)~ nW ~m^{-2} ~sr^{-1}}$ at the LORRI pivot wavelength of 0.608 $mu$m. Subtraction of the integrated light of galaxies (IGL) fainter than the photometric detection-limit from the total COB level leaves a diffuse flux component of unknown origin in the range ${rm 8.8pm4.9 (1.8 ~stat., 4.5 ~sys.) ~nW ~m^{-2} ~sr^{-1}}$ to ${rm 11.9pm4.6 (1.8 ~stat., 4.2 ~sys.) ~nW ~m^{-2} ~sr^{-1}}$. Explaining it with undetected galaxies requires the galaxy-count faint-end slope to steepen markedly at $V>24$ or that existing surveys are missing half the galaxies with $V< 30.$
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