The vortex structure of d(x2-y2)-wave superconductors is microscopically analyzed in the framework of the quasiclassical Eilenberger equations. If the pairing interaction contains an s-wave (d(xy)-wave) component in addition to a d(x2-y2)-wave component, the s-wave (d(xy)-wave) component of the order parameter is necessarily induced around a vortex in d(x2-y2)-wave superconductors. The spatial distribution of the induced s-wave and d(xy)-wave components is calculated. The s-wave component has an opposite winding number around the vortex near the d(x2-y2)-vortex core and its amplitude has the shape of a four-lobe clover. These are consistent with results based on the Ginzburg-Landau (GL) theory. The amplitude of the d(xy) component has the shape of an octofoil. The mixing of the d(xy) component cannot be explained by the GL theory, unless nonlocal correction terms are included.