The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electronic structure of FeSe across the nematic transition. We show that the self-energy corrections due to the exchange of spin fluctuations between hole and electron pockets are responsible for an orbital-dependent shrinking of the Fermi Surface that affects mainly the $xz/yz$ parts of the Fermi surface. This result is consistent with our experimental observation of the Fermi Surface in the high-temperature tetragonal phase, that includes the $xy$ electron sheet that was not clearly resolved before. In the low-temperature nematic phase, we experimentally confirm the appearance of a large ($sim$ 50meV) $xz/yz$ splittings. It can be well reproduced in our model by assuming a moderate splitting between spin fluctuations along the $x$ and $y$ crystallographic directions. Our mechanism shows how the full entanglement between orbital and spin degrees of freedom can make a spin-driven nematic transition equivalent to an effective orbital order.
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