<p>Gas-giant planets have been detected on eccentric orbits several hundreds of astronomical units in size around other stars. It has been proposed that even the Sun hosts a wide-orbit planet of 5–10 Earth masses, often called Planet Nine, which influences the dynamics of distant trans-Neptunian objects. However, the formation mechanism of such planets remains uncertain. Here we use numerical simulations to show that very-wide-orbit planets are a natural by-product of dynamical instabilities that occur in planetary systems while their host stars are still embedded in natal stellar clusters. A planet is first brought to an eccentric orbit with an apoastron of several hundred astronomical units by repeated gravitational scattering by other planets, then perturbations from nearby stellar flybys stabilize the orbit by decoupling the planet from the interaction with the inner system. In our Solar System, the two main events likely conducive to planetary scattering were the growth of Uranus and Neptune, and the giant planets instability. We estimate a 5–10% likelihood of creating a very-wide-orbit planet if either happened while the Sun was still in its birth cluster, increasing to 40% if both were. In our simulated exoplanetary systems, the trapping efficiency is 1–5%. Our results imply that planets on wide, eccentric orbits occur at least 10⁻³ per star.</p>