We report an anisotropy in the flux of cosmic rays with energies above 8 EeV observed using data recorded at the Pierre Auger Observatory with more than 12 years of operation. We consider events with zenith angles up to 80$^\circ$, so that 85% of the sky is observed, and for energies in excess of 4 EeV, for which the Observatory is fully efficient. An analysis of the first harmonic in right ascension is performed in the two energy bins 4 EeV $<E<$ 8 EeV and $E\geq$ 8 EeV. The amplitudes obtained are $0.5_{-0.2}^{+0.6}$% and $4.7_{-0.7}^{+0.9}$%, respectively. Events in the lower energy bin follow an arrival distribution consistent with isotropy. In the higher bin a significant anisotropy is found, with the measured amplitude having a $p$-value of $2.6\times 10^{-8}$ under the isotropic null hypothesis. After penalization for the fact that two different energy bins were considered, this anisotropy has a significance of $5.4\sigma$. Combining the first harmonic analysis in right ascension with another one in azimuth, which is sensitive to the dipolar component along the Earth's rotation axis, the signal above 8 EeV is well-described by a dipole with a total amplitude of $6.5_{-0.9}^{+1.3}$%. Its direction points towards Galactic coordinates $(\ell,b)=(233^\circ,-13^\circ)$, which is $\sim$125$^\circ$ from the Galactic Center, suggesting that the anisotropy has an extragalactic origin.