The B+ → Jψη′K+ decay is observed for the first time using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb−1. The branching fraction of this decay is measured relative to the known branching fraction of the B+ → ψ(2S)K+ decay and found to be: B(B+→Jψη′K+)B(B+→ψ(2S)K+)=(4.91±0.47±0.29±0.07)×10−2,B(B+→ψ(2S)K+)B(B+→Jψη′K+)​=(4.91±0.47±0.29±0.07)×10−2,where the first uncertainty is statistical, the second is systematic and the third is related to external branching fractions. A first look at the J/ψη′ mass distribution is performed and no signal of intermediate resonances is observed.[graphic not available: see fulltext]