We summarize and combine direct measurements of the mass of the $W$ boson in $sqrt{s} = 1.96 text{TeV}$ proton-antiproton collision data collected by CDF and D0 experiments at the Fermilab Tevatron Collider. Earlier measurements from CDF and D0 are combined with the two latest, more precise measurements: a CDF measurement in the electron and muon channels using data corresponding to $2.2 mathrm{fb}^{-1}$ of integrated luminosity, and a D0 measurement in the electron channel using data corresponding to $4.3 mathrm{fb}^{-1}$ of integrated luminosity. The resulting Tevatron average for the mass of the $W$ boson is $MW = 80,387 pm 16 text{MeV}$. Including measurements obtained in electron-positron collisions at LEP yields the most precise value of $MW = 80,385 pm 15 text{MeV}$.