We report the discovery of the correlated optical/X-ray low-frequency quasi-periodic oscillations (QPOs) in black hole binary SWIFT J1753.5-0127. The phase lag between two light-curves at the QPO frequency is close to zero. This result puts strong constraints on the nature of the optical emission in this object and on the origin of the QPOs in general. We demonstrate that the QPO signal and the broadband variability can be explained in terms of the hot accretion flow radiating in both optical and X-ray bands. In this model, the QPO appears due to the Lense-Thirring precession of entire flow, while the broadband variability in the optical is produced by two components: the hot flow and the irradiated disc. Using the phase-lag spectra, we put a lower limit on the orbital inclination i>50 deg, which can be used to constrain the mass of the compact object.