We analyze archival Chandra and XMM-Newton data of 4U 0142+61 within the context of the surface thermal emission and magnetospheric scattering model. We show that the 4U 0142+61 spectrum can be fit very well with this physical model that contains only four parameters. The system parameters can be tightly constrained from the fits, yielding a surface magnetic field strength of B (4.75 +/- 0.02) x 10(14) G, a surface temperature of kT 0.309 +/- 0.001 keV, and a scattering optical depth of a few in the magnetosphere. These values do not vary between observations due to the stability of the source within the window of the observations. The detailed fits yield chi(2) values that are statistically much better than the traditionally employed blackbody+power-law and two blackbody fits. The spectroscopically measured surface magnetic field strength is higher than, but within, the theoretical uncertainties of the value inferred from the dipole spin-down formula.