Free space optical (FSO) communication technology has become increasingly advanced with capabilities of high speed, high capacity, and low power consumption. However, despite the great potential of FSO, its performance is limited in a turbulent atmosphere. Atmospheric turbulence causes scintillation in the FSO propagated signals, leading to an increase in the bit error rate (BER) performance of the recovered signals at the receiver. In this paper, we demonstrate that the use of deep learning (DL) detection methods could overcome these limitations. We present a new detection method of on-off keying (OOK) modulated signals by using different models of DL over different strength FSO turbulent channels, without the need for prior knowledge of the parameters of the channel. The demonstrated DL decoders improve the performance of the FSO turbulent channel and decrease the power consumption. Moreover, the demonstrated DL models also work faster than maximum likelihood (ML) methods with perfect channel estimation decoders, with even slightly better performance because of the turbulence, thus enabling realization of FSO over turbulent atmospheric channels. INDEX TERMS Free space optical communication, deep learning, on-off keying modulation, amplitude shift keying modulation, maximum likelihood, channel state information, fully convolutional neural network, fully connected neural network, additive white gaussian noise, intensity modulation, direct detection, photodetector, bit error rate.