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We present a void clustering analysis in configuration-space using the completed Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 samples. These samples consist of Luminous Red Galaxies (LRG) combined with the high redshift tail of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) DR12 CMASS galaxies (called as LRG+CMASS sample), Emission Line Galaxies (ELG) and quasars (QSO). We build void catalogues from the three eBOSS DR16 samples using a ZOBOV-based algorithm, providing 2,814 voids, 1,801 voids and 4,347 voids in the LRG+CMASS, ELG and QSO samples, respectively, spanning the redshift range $0.6<z<2.2$. We measure the redshift space distortions (RSD) around voids using the anisotropic void-galaxy cross-correlation function and we extract the distortion parameter $β$. We test the methodology on realistic simulations before applying it to the data, and we investigate all our systematic errors on these mocks. We find $β^{\rm LRG}(z=0.74)=0.415\pm0.087$, $β^{\rm ELG}(z=0.85)=0.665\pm0.125$ and $β^{\rm QSO}(z=1.48)=0.313\pm0.134$, for the LRG+CMASS, ELG and QSO sample, respectively. The quoted errors include systematic and statistical contributions. In order to convert our measurements in terms of the growth rate $fσ_8$, we use consensus values of linear bias from the eBOSS DR16 companion papers~\citep{eBOSScosmo}, resulting in the following constraints: $fσ_8(z=0.74)=0.50\pm0.11$, $fσ_8(z=0.85)=0.52\pm0.10$ and $fσ_8(z=1.48)=0.30\pm0.13$. Our measurements are consistent with other measurements from eBOSS DR16 using conventional clustering techniques.