The branching fraction of the decay Bs0→Ds(∗)+Ds(∗)- is measured using pp collision data corresponding to an integrated luminosity of 1.0 fb-1, collected using the LHCb detector at a center-of-mass energy of 7 TeV. It is found to be B(Bs0→Ds(∗)+Ds(∗)-)=(3.05±0.10±0.20±0.34)%, where the uncertainties are statistical, systematic, and due to the normalization channel, respectively. The branching fractions of the individual decays corresponding to the presence of one or two Ds∗± are also measured. The individual branching fractions are found to be B(Bs0→Ds∗±Dsℓ)=(1.35±0.06±0.09±0.15)%, B(Bs0→Ds∗+Ds∗-)=(1.27±0.08±0.10±0.14)%. All three results are the most precise determinations to date.