Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we present the first full angular analysis in the color-suppressed modes B{sup 0}{r_arrow}J/{psi}K{sup *0} and B{sup +}{r_arrow}J/{psi}K{sup *+}. This leads to a complete determination of the decay amplitudes of these modes including the longitudinal polarization {Gamma}{sub L}/{Gamma}=0.52{plus_minus}0.07{plus_minus}0.04 and the P wave component {vert_bar}P{vert_bar}{sup 2}=0.16{plus_minus}0.08{plus_minus}0.04. In addition, we update the branching fractions for B{r_arrow}J/{psi}K and B{r_arrow}J/{psi}K{sup *}. {copyright} {ital 1997} {ital The American Physical Society}