The Fermi Large Area Telescope (LAT) has an instantaneous field of view (FoV) covering $\sim 1/5$ of the sky and it completes a survey of the entire sky in high-energy gamma-rays every 3 hr. It enables searches for transient phenomena over timescales from milliseconds to years. Among these phenomena could be electromagnetic counterparts to gravitational wave (GW) sources. In this paper, we present a detailed study of the LAT observations relevant to Laser Interferometer Gravitational-wave Observatory (LIGO) event GW150914, which is the first direct detection of gravitational waves and has been interpreted as being due to the coalescence of two stellar-mass black holes. The localization region for GW150914 was outside the LAT FoV at the time of the GW signal. However, as part of routine survey observations, the LAT observed the entire LIGO localization region within ~70 minutes of the trigger and thus enabled a comprehensive search for a γ-ray counterpart to GW150914. The study of the LAT data presented here did not find any potential counterparts to GW150914, but it did provide limits on the presence of a transient counterpart above 100 MeV on timescales of hours to days over the entire GW150914 localization region.Read less <