This study provides an analysis of atmospheric neutrino oscillations at the ESSnuSB far detector facility. The prospects of the two cylindrical Water Cherenkov detectors with a total fiducial mass of 540 kt are investigated over 10 years of data taking in the standard three-flavor oscillation scenario. We present the confidence intervals for the determination of mass ordering, θ23 octant as well as for the precisions on sin2θ23 and Δm312. It is shown that mass ordering can be resolved by 3σ CL (5σ CL) after 4 years (10 years) regardless of the true neutrino mass ordering. Correspondingly, the wrong θ23 octant could be excluded by 3σ CL after 4 years (8 years) in the case where the true neutrino mass ordering is normal ordering (inverted ordering). The results presented in this work are complementary to the accelerator neutrino program in the ESSnuSB project.