Understanding the effect of ocean turbulence on optical beam propagation is critical to the design and performance evaluation of underwater wireless optical communication systems. In this Letter, we propose a unified Weibull-generalized gamma distribution to characterize the laser beam irradiance fluctuations of turbulent underwater thermocline wireless optical channels. The proposed model shows an excellent agreement with the measured data under various experimental emulated channel conditions that cover turbulences induced by temperature, salinity, and air bubbles. To the best of our knowledge, this is the first model that comprehensively describes the statistics of the laser beam irradiance fluctuations in underwater wireless optical channels due to both thermohaline gradient and air bubbles.