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The electron paramagnetic resonance (EPR) study of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ crystals gives evidence that donors can be regarded as ${\mathrm{O}}^{2\ensuremath{-}}$ vacancies trapping single electrons. The Lorentzian line shape of the EPR spectra observed in the range of 5--300 K, which exhibit anisotropic g values, suggests that motional narrowing occurs in this temperature range. For any magnetic-field orientation a single EPR line is observed, indicating that donor electrons are predominantly created in one of the three different oxygen sites in the $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ crystal. A previous transmission electron microscopy study suggested that a break of symmetry in domains of 2--3 nm correlates with a preceding cluster model of oxygen vacancies. From the temperature dependence of the EPR linewidth and the electrical conductivity it is found that the electron conduction in the clusters and/or between them is governed by a tunneling process at low temperatures, whereas at temperatures above 50 K, the transport of electrons through hopping between the clusters is thermally activated.