Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband—optical through X-ray—spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring precession of the hot accretion flow, whose outer parts radiate in optical wavelengths. At the same time, its innermost parts are emitting X-rays, which explains the observed connection of QPO periods. We predict that the X-ray and optical QPOs should be either in phase or shifted by half a period, depending on the observer position. We investigate the QPO harmonic content and find that the variability amplitudes at the fundamental frequency are larger in the optical, while the X-rays are expected to have strong harmonics. We then discuss the QPO spectral dependence and compare the expectations to the existing data.