We detail the sensitivity of the proposed liquid xenon DARWIN observatory to solar neutrinos via elastic electron scattering. We find that DARWIN will have the potential to measure the fluxes of five solar neutrino components: pp, 7Be, 13N, 15O and pep. The precision of the 13N, 15O and pep components is hindered by the double-beta decay of 136Xe and, thus, would benefit from a depleted target. A high-statistics observation of pp neutrinos would allow us to infer the values of the electroweak mixing angle, sin2θw, and the electron-type neutrino survival probability, Pee, in the electron recoil energy region from a few keV up to 200 keV for the first time, with relative precision of 5% and 4%, respectively, with 10 live years of data and a 30 tonne fiducial volume. An observation of pp and 7Be neutrinos would constrain the neutrino-inferred solar luminosity down to 0.2%. A combination of all flux measurements would distinguish between the high- (GS98) and low-metallicity (AGS09) solar models with 2.1–2.5σ significance, independent of external measurements from other experiments or a measurement of 8B neutrinos through coherent elastic neutrino-nucleus scattering in DARWIN. Finally, we demonstrate that with a depleted target DARWIN may be sensitive to the neutrino capture process of 131Xe.