In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb–Pb collisions at the LHC provide an accurate measurement of kaon–proton scattering parameters at low relative momentum, allowing precise access to the K⁻p→K⁻p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K⁻p(K⁺p‾) and K⁺p(K⁻p‾) pairs in Pb–Pb collisions at centre-of-mass energy per nucleon pair of s_NN=5.02 TeV registered by the ALICE experiment is reported. The components of the K⁻p complex scattering length are extracted and found to be ℜf₀=−0.91±0.03(stat)_−0.03^+0.17(syst) and ℑf₀=0.92±0.05(stat)_−0.33^+0.12(syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.