A measurement of the branching fraction of the decay is performed using proton–proton collision data corresponding to an integrated luminosity of collected by the LHCb experiment between 2011 and 2016. The branching fraction is determined to be B(Bs0→KS0KS0)=[8.3±1.6(stat)±0.9(syst)±0.8(norm)±0.3(fs/fd)]×10-6, where the first uncertainty is statistical, the second is systematic, and the third and fourth are due to uncertainties on the branching fraction of the normalization mode and the ratio of hadronization fractions . This is the most precise measurement of this branching fraction to date. Furthermore, a measurement of the branching fraction of the decay is performed relative to that of the channel, and is found to be B(B0→KS0KS0)B(Bs0→KS0KS0)=[7.5±3.1(stat)±0.5(syst)±0.3(fs/fd)]×10-2.