The first observation of the Bs0​→ D∗+D∗− decay and the measurement of its branching ratio relative to the B0→ D∗+D∗− decay are presented. The data sample used corresponds to an integrated luminosity of 9 fb−1−1 of proton-proton collisions recorded by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018. The decay is observed with more than 10 standard deviations and the time-integrated ratio of branching fractions is determined to be B(Bs0→D∗+D∗−)B(B0→D∗+D∗−)=0.269±0.032±0.011±0.008, where the first uncertainty is statistical, the second systematic and the third due to the uncertainty of the fragmentation fraction ratio fs​/fd​. The Bs0​→ D∗+D∗− branching fraction is calculated to be B(Bs0→D∗+D∗−)=(2.15±0.26±0.09±0.06±0.16)×10−4, where the fourth uncertainty is due to the B0→ D∗+D∗− branching fraction. These results are calculated using the average Bs0​ meson lifetime in simulation. Correction factors are reported for scenarios where either a purely heavy or a purely light Bs0​ eigenstate is considered. [graphic not available: see fulltext]