The cosmic-ray fluxes of electrons and positrons (e ± ) are measured with high precision by the space-borne particle spectrometer AMS-02. To infer a precise interpretation of the production processes for e ± in our Galaxy, it is necessary to have an accurate description of the secondary component, produced by the interaction of cosmic-ray proton and helium with the interstellar medium atoms. We determine new analytical functions of the Lorentz invariant cross section for the production of π ± and K ± by fitting data from collider experiments. We also evaluate the invariant cross sections for several other channels, involving for example hyperon decays, contributing at the few % level on the total cross section. For all these particles, the relevant 2 and 3 body decay channels are implemented, with the polarized µ ± decay computed with next-to-leading order corrections. The cross section for scattering of nuclei heavier than protons is modeled by fitting data on p + C collisions. The total differential cross section dσ/dT e ± (p + p → e ± + X) is predicted from 10 MeV up to 10 TeV of e ± energy with an uncertainty of about 5-7% in the energies relevant for AMS-02 positron flux, thus dramatically reducing the precision of the theoretical model with respect to the state of the art. Finally, we provide a prediction for the secondary Galactic e ± source spectrum with an uncertainty of the same level. As a service for the scientific community, we provide numerical tables and a script to calculate energy-differential cross sections.