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We determine the [O III]λ5007 equivalent width (EW) distribution of 1.700\lt \rm {z}\lt 2.274 rest-frame ultraviolet (UV)-selected (M_UV < -19) star-forming galaxies in the GOODS North and South fields. We make use of deep HDUV broad-band photometry catalogues for selection and 3D-HST WFC3/IR grism spectra for measurement of line properties. The [O III]λ5007 EW distribution allows us to measure the abundance of extreme emission line galaxies (EELGs) within this population. We model a lognormal distribution to the [O III]λ5007 rest-frame EWs of galaxies in our sample, with location parameter µ = 4.24 ± 0.07 and variance parameter σ = 1.33 ± 0.06. This EW distribution has a mean [O III]λ5007 EW of 168 ± 1 Å. The fractions of \rm {z}\sim 2 rest-UV-selected galaxies with [O III]λ5007 EWs greater than 500, 750, and 1000 Å are measured to be 6.8^{+1.0}_{-0.9}{{\ \rm per\ cent}}, 3.6^{+0.7}_{-0.6}{{\ \rm per\ cent}}, and 2.2^{+0.5}_{-0.4}{{\ \rm per\ cent}}, respectively. The EELG fractions do not vary strongly with UV luminosity in the range (-21.6 < M_UV < -19.0) considered in this paper, consistent with findings at higher redshifts. We compare our results to \rm {z}\sim 5 and \rm {z}\sim 7 studies, where candidate EELGs have been discovered through Spitzer/IRAC colours, and we identify rapid evolution with redshift in the fraction of star-forming galaxies observed in an extreme emission line phase (a rise by a factor ∼10 between \rm {z}\sim 2 and \rm {z}\sim 7). This evolution is consistent with an increased incidence of strong bursts in the galaxy population of the reionization era. While this population makes a sub-dominant contribution of the ionizing emissivity at \rm {z}\simeq 2, EELGs are likely to dominate the ionizing output in the reionization era.