We report the measurement of sub-MeV solar neutrinos through the use of their associated Cherenkov radiation, performed with the Borexino detector at the Laboratori Nazionali del Gran Sasso. The measurement is achieved using a novel technique that correlates individual photon hits of events to the known position of the Sun. In an energy window between 0.54 MeV to 0.74 MeV, selected using the dominant scintillation light, we have measured 10887$^{+2386}_{-2103} (\mathrm{stat.})\pm 947 (\mathrm{syst.})$ ($68\%$ confidence interval) solar neutrinos out of 19904 total events. This corresponds to a $^{7}$Be neutrino interaction rate of 51.6$^{+13.9}_{-12.5}$ counts/(day$\cdot$ 100 ton), which is in agreement with the Standard Solar Model predict...