Fully reconstructed View the MathML sourcett→W+bW−b→ℓνqq′bb events are used to determine the fractions of right-handed (f+f+) and longitudinally polarized (f0f0) W bosons produced in top-quark decays. The helicity fractions are sensitive to the couplings and the Dirac structure of the Wtb vertex. This Letter reports measurements of the W-boson helicity fractions from two different methods using data corresponding to an integrated luminosity of View the MathML source1.9fb−1 of View the MathML sourcepp collisions at a center-of-mass energy of 1.96 TeV collected by the CDF II detector operating at the Fermilab Tevatron. Combining the results from the two methods, we find f0=0.62±0.10(stat)±0.05(syst)f0=0.62±0.10(stat)±0.05(syst) under the assumption that f+=0f+=0, and f+=−0.04±0.04(stat)±0.03(syst)f+=−0.04±0.04(stat)±0.03(syst) with f0f0 fixed to the theoretically expected value of 0.70. Model-independent fits are also performed and simultaneously determine f0=0.66±0.16(stat)±0.05(syst)f0=0.66±0.16(stat)±0.05(syst) and f+=−0.03±0.06(stat)±0.03(syst)f+=−0.03±0.06(stat)±0.03(syst). All these results are consistent with standard model expectations.