The B+→Ds+Ds-K+ decay is observed for the first time using proton-proton collision data collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9  fb-1. Its branching fraction relative to that of the B+→D+D-K+ decay is measured to be B(B+→Ds+Ds-K+)B(B+→D+D-K+)=0.525±0.033±0.027±0.034, where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the Ds±→K∓K±π± and D±→K∓π±π± decays. This measurement fills an experimental gap in the knowledge of the family of Cabibbo-favored b¯→c¯cs¯ transitions and opens the path for unique studies of spectroscopy in future.