The OTELO survey is a very deep, blind exploration of a selected region of the Extended Groth Strip and is designed for finding emission-line sources (ELSs). The survey design, observations, data reduction, astrometry, and photometry, as well as the correlation with ancillary data used to obtain a final catalogue, including photo-z estimates and a preliminary selection of ELS, were described in a previous contribution. Here, we aim to determine the main properties and luminosity function (LF) of the [O III] ELS sample of OTELO as a scientific demonstration of its capabilities, advantages, and complementarity with respect to other surveys. The selection and analysis procedures of ELS candidates obtained using tunable filter (TF) pseudo-spectra are described. We performed simulations in the parameter space of the survey to obtain emission-line detection probabilities. Relevant characteristics of [O III] emitters and the LF([O III]), including the main selection biases and uncertainties, are presented. A total of 184 sources were confirmed as [O III] emitters at a mean redshift z=0.83. The minimum detectable line flux and equivalent width (EW) in this ELS sample are $sim$5 $times$ 10$^{-19}$ erg s$^{-1}$ cm$^{2}$ and $sim$6 AA, respectively. We are able to constrain the faint-end slope ($alpha = -1.03pm0.08$) of the observed LF([O III]) at z=0.83. This LF reaches values that are approximately ten times lower than those from other surveys. The vast majority (84%) of the morphologically classified [O III] ELSs are disc-like sources, and 87% of this sample is comprised of galaxies with stellar masses of M$_star$ $<$ 10$^{10}$ M$_{odot}$.
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