We present the first measurement of nuclear recoils from solar ^{8}B neutrinos via coherent elastic neutrino-nucleus scattering with the XENONnT dark matter experiment. The central detector of XENONnT is a low-background, two-phase time projection chamber with a 5.9 t sensitive liquid xenon target. A blind analysis with an exposure of 3.51 t×yr resulted in 37 observed events above 0.5 keV, with (26.4_{-1.3}^{+1.4}) events expected from backgrounds. The background-only hypothesis is rejected with a statistical significance of 2.73σ. The measured ^{8}B solar neutrino flux of (4.7_{-2.3}^{+3.6})×10^{6} cm^{-2} s^{-1} is consistent with results from the Sudbury Neutrino Observatory. The measured neutrino flux-weighted CEνNS cross section on Xe of (1.1_{-0.5}^{+0.8})×10^{-39} cm^{2} is consistent with the Standard Model prediction. This is the first direct measurement of nuclear recoils from solar neutrinos with a dark matter detector.