We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of 343 708 spectroscopically confirmed quasars between redshift 0.8 < z < 2.2 are used as tracers of the underlying dark matter field. In comparison with DR14 sample, the final sample doubles the number of objects as well as the survey area. In this paper, we present the analysis in configuration space by measuring the two-point correlation function and decomposing it using the Legendre polynomials. For the full-shape analysis of the Legendre multipole moments, we measure the baryon acoustic oscillation (BAO) distance and the growth rate of the cosmic structure. At an effective redshift of z(eff) = 1.48, we measure the comoving angular diameter distance D-M(z(eff))/r(drag) = 30.66 +/- 0.88, the Hubble distance D-H(z(eff))/r(drag) = 13.11 +/- 0.52, and the product of the linear growth rate and the rms linear mass fluctuation on scales of 8 h(-1) Mpc, f sigma(8)(z(eff)) = 0.439 +/- 0.048. The accuracy of these measurements is confirmed using an extensive set of mock simulations developed for the quasar sample. The uncertainties on the distance and growth rate measurements have been reduced substantially (similar to 45 and similar to 30 per cent) with respect to the DR14 results. We also perform a BAO-only analysis to cross check the robustness of the methodology of the full-shape analysis. Combining our analysis with the Fourier-space analysis, we arrive at D-M(c)(z(eff))/r(drag) = 30.21 +/- 0.79, D-H(c) (z(eff))/r(drag) = 13.23 +/- 0.47, and f sigma(c)(8) (z(eff)) = 0.462 +/- 0.045.