As the first detections of Gravitational Waves (GW) from the coalescence of compact objects were announced by LIGO and Virgo, a new era for astronomy began. Searches for electromagnetic (EM) counterparts of GW events are of fundamental importance, as their success will increase the confidence in the GW detection and will help characterize the system parameters. The Fermi Gamma-ray Space Telescope is the most capable observatory to simultaneously observe a large fraction of the sky from 10 keV to more than 300 GeV, providing the unique capability of rapidly covering the entire probability region from a LIGO candidate. In this paper, we will present the strategy for follow-up observations of GW events with the Fermi Large Area Telescope (LAT), focusing on the results from the first science runs O1/O2. We will also discuss the prospects for detections of GW in coincidence with a gamma-ray signal from the Fermi Gamma-ray Burst Monitor (GBM) and the LAT, likely from a short Gamma-Ray Burst (sGRB) arising from the merger of two neutron stars.