We measure the polarization of W bosons from top-quark (t) decays into final states with a charged lepton and jets, tt̅ →W+bW-b̅ →ℓνbqq̅ ′b̅ , 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