A vibronic exciton model is applied to explain the long-lived oscillatory features in the two-dimensional (2D) electronic spectra of the Fenna–Matthews–Olson (FMO) complex. Using experimentally determined parameters and uncorrelated site energy fluctuations, the model predicts oscillations with dephasing times of 1.3 ps at 77 K, which is in a good agreement with the experimental results. These long-lived oscillations originate from the coherent superposition of vibronic exciton states with dominant contributions from vibrational excitations on the same pigment. The oscillations obtain a large amplitude due to excitonic intensity borrowing, which gives transitions with strong vibronic character a significant intensity despite the small Huang–Rhys factor. Purely electronic coherences are found to decay on a 200 fs time scale.