We report on a measurement of astrophysical tau neutrinos with 9.7 years of IceCube data. Using convolutional neural networks trained on images derived from simulated events, seven candidate \(\nu_\tau\) events were found with visible energies ranging from roughly 20 TeV to 1 PeV and a median expected parent \(\nu_\tau\) energy of about 200 TeV. Considering backgrounds from astrophysical and atmospheric neutrinos, and muons from \(\pi^\pm/K^\pm\) decays in atmospheric air showers, we obtain a total estimated background of about 0.5 events, dominated by non-\(\nu_\tau\) astrophysical neutrinos. Thus, we rule out the absence of astrophysical \(\nu_\tau\) at the \(5\sigma\) level. The measured astrophysical \(\nu_\tau\) flux is consistent with expectations based on previously published IceCube astrophysical neutrino flux measurements and neutrino oscillations.