The Belle II detector at the SuperKEKB e+e- collider started its operation in April 2018. We describe a system used at the Belle II experiment for the on-line measurement of the luminosity provided by the collider utilizing elastic e^+e^- Bhabha scattering and two-photon annihilation processes. A statistical accuracy of 5% has been achieved at the luminosity of 1034 cm-2s-1 with a counting rate of about 1 Hz. The overall systematic uncertainty is estimated to be at the level of 1.7%. Comparison with offline results is also presented.