The spin susceptibility of strongly correlated Sr2RuO4 is known to display a rich structure in reciprocal space, with a prominent peak at Q(i) = (0.3,0.3,0). It is still debated if the resulting incommensurate spin-density-wave fluctuations foster unconventional superconductivity at low temperature or compete therewith. By means of density functional theory combined with dynamical mean-field theory, we reveal the realistic multi-orbital signature of the (dynamic) spin susceptibility beyond existing weak-coupling approaches. The experimental fluctuation spectrum up to 80 meV is confirmed by theory. Furthermore, the peak at Q(i) is shown to carry nearly equal contributions from each of the Ru(4d)-t(2)g orbitals, pointing to a cooperative effect resulting in the dominant spin fluctuations. Copyright (C) EPLA, 2018