In this paper, we evaluate the end-to-end bit error rate (BER) of point-to-point underwater wireless optical communication (UWOC) systems with multi-hop transmission. To do so, we analytically derive the BER expression of a single-hop UWOC link as the building block for end-to-end BER evaluation. We also apply photon-counting method to evaluate the system BER in the presence of shot noise. Moreover, we use Gauss-Hermite quadrature formula to obtain the closed-form solutions for the system BER in the case of log-normal underwater fading channels. Our analytical treatment involves all the impairing effects of the underwater optical channel, namely absorption, scattering and fading. Numerical results demonstrate that multi-hop transmission by alleviating the aforementioned impairing effects of the channel, can significantly improve the system performance and extend the viable end-to-end communication distance. For example, dual-hop transmission in $22.5$ m and $45$ m coastal water links can provide $17.5$ dB and $39$ dB performance enhancement at the BER of $10^{-6}$, respectively.