The extragalactic background light (EBL) includes photons with wavelengths from ultraviolet to infrared, which are effective at attenuating gamma rays with energy above ~10 GeV during propagation from sources at cosmological distances. This results in a redshift- and energy-dependent attenuation of the γ-ray flux of extragalactic sources such as blazars and gamma-ray bursts (GRBs). The Large Area Telescope on board Fermi detects a sample of γ-ray blazars with redshift up to z ~ 3, and GRBs with redshift up to z ~ 4.3. Using photons above 10 GeV collected by Fermi over more than one year of observations for these sources, we investigate the effect of γ-ray flux attenuation by the EBL. We place upper limits on the γ-ray opacity of the universe at various energies and redshifts and compare this with predictions from well-known EBL models. We find that an EBL intensity in the optical-ultraviolet wavelengths as great as predicted by the "baseline" model of Stecker et al. can be ruled out with high confidence.