We measure the polarization of W bosons from top-quark (t) decays into final states with a charged lepton and jets, tt→W+bW−b→ℓνbqq′b, using the full Run II data set collected by the CDF II detector, corresponding to an integrated luminosity of 8.7  fb−1. A model-independent method simultaneously determines the fraction of longitudinal (f0) and right-handed (f+) W bosons to yield f0=0.726±0.066(stat)±0.067(syst) and f+=−0.045±0.044(stat)±0.058(syst) with a correlation coefficient of −0.69. Additional results are presented under various standard model assumptions. No significant discrepancies with the standard model are observed.