The nuclear magnetic moment of Li-9 and the quadrupole moments of Li-8 and Li-9 have been measured by use of the beta-asymmetry detection of nuclear magnetic resonance on optically polarized beams at ISOLDE/CERN. The radioactive beams were implanted in Si for g-factor measurements and in Zn, LiNbO3, and LiTaO3 crystals for quadrupole moment measurements. The electric-field gradient V-zz=4.26(4)x10(15) V/cm(2) is deduced for Li in Zn. Using a recently adopted reference value, Q(Li-7)=-40.0(3) mb, we reevaluated all earlier reported nuclear quadrupole moments of Li-8 and Li-9. Based on all available previous and present data, the adopted quadrupole moments for these isotopes are Q(Li-8)=+31.4(2) mb and Q(Li-9)=-30.6(2) mb. The magnetic moment of Li-9 is deduced as mu(Li-9)=3.43678(6)mu(N). The values are compared with predictions from shell-model and cluster-model calculations.