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 √sNN=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.