The ALICE Collaboration reports the measurement of semi-inclusive distributions of charged-particle jets recoiling from a high transverse momentum (high$p_{\mathrm{T}}$) hadron trigger in proton-proton and central Pb-Pb collisions at$\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. A data-driven statistical method is used to mitigate the large uncorrelated background in central Pb-Pb collisions. Recoil jet distributions are reported for jet resolution parameter$R=0.2$, 0.4, and 0.5 in the range$7<p_{\mathrm{T},\text{jet}}<140\mathrm{GeV}/c$and trigger-recoil jet azimuthal separation$\pi /2<\mathrm{\Delta }\phi <\pi$. The measurements exhibit a marked medium-induced jet yield enhancement at low$p_{\mathrm{T}}$and at large azimuthal deviation from$\mathrm{\Delta }\phi \sim \pi$. The enhancement is characterized by its dependence on$\mathrm{\Delta }\phi$, which has a slope that differs from zero by$4.7\sigma$. Comparisons to model calculations incorporating different formulations of jet quenching are reported. These comparisons indicate that the observed yield enhancement arises from the response of the QGP medium to jet propagation.