Abstract Rare two-body decays of the top quark into a neutral bottom-quark meson plus an up- or charm-quark: $$ t\to {\overline{B}}^0+u,\kern0.5em c;t\to {\overline{B}}_s^0+c,\kern0.5em u $$ t → B ¯ 0 + u , c ; t → B ¯ s 0 + c , u ; and t → ϒ(nS) + c, u, are studied for the first time. The corresponding partials widths are computed at leading order in the non-relativistic QCD framework. The sums of all two-body branching ratios amount to $$ \mathrm{\mathcal{B}}\left(t\to {\overline{B}}^0+\mathrm{jet}\right)\approx \mathrm{\mathcal{B}}\left(t\to {\overline{B}}_s^0+\mathrm{jet}\right)\approx 4.2\cdot {10}^{-5} $$ ℬ t → B ¯ 0 + jet ≈ ℬ t → B ¯ s 0 + jet ≈ 4.2 ⋅ 10 − 5 and ℬ(t → ϒ(nS) + jet) ≈ 2 ⋅ 10−9, respectively. The feasibility to observe the $$ t\to {\overline{B}}_{(s)}^0+ $$ t → B ¯ s 0 + jet decay is estimated in top- pair events produced in proton-proton collisions at $$ \sqrt{s} $$ s = 14, 100 TeV at the LHC and FCC, respectively. Combining many exclusive hadronic $$ {\overline{B}}_{(s)}^0 $$ B ¯ s 0 decays, with J/ψ or D0,± final states, about 50 (16 000) events are expected in 3 (20) ab−1 of integrated luminosity at the LHC (FCC), after typical selection criteria, acceptance, and efficiency losses. An observation of the two-body top-quark decay can also be achieved in the interesting t → b(jet) + c(jet) dijet final state, where the $$ {\overline{B}}_{(s)}^0 $$ B ¯ s 0 decay products are reconstructed as a jet, with 5 300 and 1.4 million signal events above backgrounds expected after selection criteria at the LHC and FCC, respectively. Such unique final states provide a new direct method to precisely measure the top-quark mass via simple 2-body invariant mass analyses.