A design study, named ESS νSB for European Spallation Source neutrino Super Beam, has been carried out during the years 2018–2022 of how the 5 MW proton linear accelerator of the European Spallation Source under construction in Lund, Sweden, can be used to produce the world’s most intense long-baseline neutrino beam. The high beam intensity will allow for measuring the neutrino oscillations near the second oscillation maximum at which the CP violation signal is close to three times higher than at the first maximum, where other experiments measure. This will enable CP violation discovery in the leptonic sector for a wider range of values of the CP violating phase δCP and, in particular, a higher precision measurement of δCP. The present Conceptual Design Report describes the results of the design study of the required upgrade of the ESS linac, of the accumulator ring used to compress the linac pulses from 2.86 ms to 1.2 μs, and of the target station, where the 5 MW proton beam is used to produce the intense neutrino beam. It also presents the design of the near detector, which is used to monitor the neutrino beam as well as to measure neutrino cross sections, and of the large underground far detector located 360 km from ESS, where the magnitude of the oscillation appearance of νe from νμ is measured. The physics performance of the ESS νSB research facility has been evaluated demonstrating that after 10 years of data-taking, leptonic CP violation can be detected with more than 5 standard deviation significance over 70% of the range of values that the CP violation phase angle δCP can take and that δCP can be measured with a standard error less than 8° irrespective of the measured value of δCP. These results demonstrate the uniquely high physics performance of the proposed ESS νSB research facility.