In an electronic nematic phase, electrons spontaneously break the rotational point-group symmetry of the crystal. Iron based superconductors have recently provided remarkable examples for such behaviors. Indeed, the electronic properties manifest a much larger anisotropy across the tetragonal to orthorhombic transition than expected from the structural changes alone. One possibility is that the nematic phase is a precursor of the antiferromagnetic order that usually emerges at lower temperature by selecting an ordering wave vector along the x direction. On the other hand, direct measurements of the band structure seem to point to a true symmetry-breaking state with a charge unbalance between the xz and yz orbitals. Here we use accurate ARPES measurements in FeSe, supported by detailed microscopic calculations, to show that an orbital-dependent shrinking of the Fermi surface is the key mechanism able to describe the temperature evolution of the electronic structure across the structural transition. In this picture, the full entanglement between orbital and spin degrees of freedom converts the anisotropy of the spin fluctuations into an effective orbital order.