We summarize and combine direct measurements of the mass of the W boson in s√=1.96  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  fb−1 of integrated luminosity, and a D0 measurement in the electron channel using data corresponding to 4.3  fb−1 of integrated luminosity. The resulting Tevatron average for the mass of the W boson is MW=80387±16  MeV. Including measurements obtained in electron-positron collisions at LEP yields the most precise value of MW=80385±15  MeV.