In this paper, we consider the problem of detection of on-off keying signals in free-space optical communication links over weak atmospheric turbulence conditions, which causes variations in the intensity and phase of the received light signal. Fading in signal due to the weak atmospheric turbulence can be modeled by a lognormal distribution, to a sufficient degree of accuracy. Assuming only the knowledge of statistics of fading, we derive the near-optimal, blind detection rule exploiting the fact that the parameter of the lognormal distribution is small in practice. We also obtain the expression for the corresponding detection threshold in closed-form. This simple technique offers benefits over other existing detection strategies, as it has a low computational complexity. Through Monte Carlo simulations, we validate the accuracy of our expressions, and show that the performances of the optimal detector and the derived detector are nearly equal for low parameter values.