The top quark is the heaviest known elementary particle, with a mass about 40 times larger than the mass of its isospin partner, the bottom quark. It decays almost 100% of the time to a $W$ boson and a bottom quark. Using top-antitop pairs at the Tevatron proton-antiproton collider, the CDF and {\dzero} collaborations have measured the top quark's mass in different final states for integrated luminosities of up to 5.8 fb$^{-1}$. This paper reports on a combination of these measurements that results in a more precise value of the mass than any individual decay channel can provide. It describes the treatment of the systematic uncertainties and their correlations. The mass value determined is 173.18 \pm 0.56 \thinspace ({\rm stat}) \pm 0.75 \thinspace ({\rm syst}) GeV or $173.18 \pm 0.94$ GeV, which has a precision of $\pm 0.54$, making this the most precise determination of the top quark mass.

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