The decays Bs0 --> Ds(*)+ Ds(*)- are reconstructed in a data sample corresponding to an integrated luminosity of 6.8 fb-1 collected by the CDF II detector at the Tevatron pbar{p} collider. All decay modes are observed with a significance of more than 10 sigma, and we measure the Bs0 production rate times Bs0 --> Ds(*)+ Ds(*)- branching ratios relative to the normalization mode B0 --> Ds+ D- to be $0.183 pm 0.021 pm 0.017$ for Bs0 --> Ds+ Ds-, $0.424 pm 0.046 pm 0.035$ for Bs0 --> Ds*+- Ds-+, $0.654 pm 0.072 pm 0.065$ for Bs0 --> Ds*+ Ds*-, and $1.261 pm 0.095 pm 0.112$ for the inclusive decay Bs0 --> Ds(*)+ Ds(*)-, where the uncertainties are statistical and systematic. These results are the most precise single measurements to date and provide important constraints for indirect searches for non-standard model physics in Bs0 mixing.
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