We report observation of the electroweak production of single top quarks in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ based on $2.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected by the D0 detector at the Fermilab Tevatron Collider. Using events containing an isolated electron or muon and missing transverse energy, together with jets originating from the fragmentation of $b$ quarks, we measure a cross section of $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}tb+X,tqb+X)=3.94\ifmmode\pm\else\textpm\fi{}0.88\text{ }\text{ }\mathrm{pb}$. The probability to measure a cross section at this value or higher in the absence of signal is $2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, corresponding to a 5.0 standard deviation significance for the observation.