  We present measurements of the anisotropic cross-correlation of galaxies and
cosmic voids in data from the Sloan Digital Sky Survey Main Galaxy Sample
(MGS), Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS)
luminous red galaxy catalogues from SDSS Data Releases 7, 12 and 16, covering
the redshift range $0.07<z<1.0$. As in our previous work analysing voids in
subsets of these data, we use a reconstruction method applied to the galaxy
data before void-finding in order to remove selection biases when constructing
the void samples. We report results of a joint fit to the multipole moments of
the measured cross-correlation for the growth rate of structure,
$f\sigma_8(z)$, and the ratio $D_\mathrm{M}(z)/D_\mathrm{H}(z)$ of the comoving
angular diameter distance to the Hubble distance, in six redshift bins. For
$D_\mathrm{M}/D_\mathrm{H}$, we are able to achieve a significantly higher
precision than that obtained from analyses of the baryon acoustic oscillations
(BAO) and galaxy clustering in the same datasets. Our growth rate measurements
are of lower precision but still comparable with galaxy clustering results. For
both quantities, the results agree well with the expectations for a
$\Lambda$CDM model. Assuming a flat Universe, our results correspond to a
measurement of the matter density parameter
$\Omega_\mathrm{m}=0.337^{+0.026}_{-0.029}$. For more general models the
degeneracy directions obtained are consistent with and complementary to those
from other cosmological probes. These results consolidate void-galaxy
cross-correlation measurements as a pillar of modern observational cosmology.
