Free-space optics naturally offers multiple-channel communications and sensing exploitable in many applications. The different optical beams will, however, generally be overlapping at the receiver, and, especially with atmospheric turbulence or other scattering or aberrations, the arriving beam shapes may not even be known in advance. We show that such beams can be still separated in the optical domain, and simultaneously detected with negligible cross-talk, even if they share the same wavelength and polarization, and even with unknown arriving beam shapes. The kernel of the adaptive multibeam receiver presented in this work is a programmable integrated photonic processor that is coupled to free-space beams through a two-dimensional array of optical antennas. We demonstrate separation of beam pairs arriving from different directions, with overlapping spatial modes in the same direction, and even with mixing between the beams deliberately added in the path. With the circuit’s optical bandwidth of more than 40 nm, this approach offers an enabling technology for the evolution of FSO from single-beam to multibeam space-division multiplexed systems in a perturbed environment, which has been a game-changing transition in fiber-optic systems.