Indoor positioning or localization based on visible light communications (VLC) is an emerging technology with wide applications. In conventional localization schemes, the trilateration technique is widely used with at least three separate lighting sources to determine the user’s location. An indoor VLC positioning scheme based on the optical power distributions of only two light emitting diodes (LEDs) is reported for different environments. We have used two received signal strength indications to determine the user’s position based on the LEDs configuration offering less complexity. We propose comprehensive mathematical models for the VLC localization system considering the noise and its impact on the user’s location, and numerically evaluated it over a range of signal-to-noise ratios (SNRs). In addition, it is compared to the results with the exiting trilateration technique. The performance of the proposed system is evaluated with a reported accuracy of 13 dB.