We report measurements of the polarization of W bosons from top-quark decays using 2.7 fb{-1} of pp collisions collected by the CDF II detector. Assuming a top-quark mass of 175 GeV/c{2}, three measurements are performed. A simultaneous measurement of the fraction of longitudinal (f{0}) and right-handed (f{+}) W bosons yields the model-independent results f{0}=0.88±0.11(stat)±0.06(syst) and f{+}=-0.15±0.07(stat)±0.06(syst) with a correlation coefficient of -0.59. A measurement of f{0} [f{+}] constraining f{+} [f{0}] to its standard model value of 0.0 [0.7] yields f{0}=0.70±0.07(stat)±0.04(syst) [f{+}=-0.01±0.02(stat)±0.05(syst)]. All these results are consistent with standard model expectations. We achieve the single most precise measurements of f{0} for both the model-independent and model-dependent determinations.