Our Galaxy hosts the annihilation of a few 10⁴³ low-energy positrons every second. Radioactive isotopes capable of supplying such positrons are synthesized in stars, stellar remnants and supernovae. For decades, however, there has been no positive identification of a main stellar positron source, leading to suggestions that many positrons originate from exotic sources like the Galaxy’s central supermassive black hole or dark matter annihilation. Here we show that a single type of transient source, deriving from stellar populations of age 3–6 Gyr and yielding ∼0.03 M⊙ of the positron emitter ⁴⁴Ti, can simultaneously explain the strength and morphology of the Galactic positron annihilation signal and the Solar System abundance of the ⁴⁴Ti dec...