Particle energization in shear flows is invoked to explain nonthermal emission from the boundaries of relativistic astrophysical jets. Yet the physics of particle injection, i.e., the mechanism that allows thermal particles to participate in shear-driven acceleration, remains unknown. With particle-in-cell simulations, we study the development of Kelvin–Helmholtz (KH) instabilities seeded by the velocity shear between a relativistic magnetically dominated electron–positron jet and a weakly magnetized electron–ion ambient plasma. We show that, in their nonlinear stages, KH vortices generate kinetic-scale reconnection layers, which efficiently energize the jet particles, thus providing a first-principles mechanism for particle injection into shear-driven acceleration. Our work lends support to spine-sheath models of jet emission—with a fast core/spine surrounded by a slower sheath —and can explain the origin of radio-emitting electrons at the boundaries of relativistic jets.