We have searched for radio pulsations towards 49 Fermi Large Area Telescope (LAT) 1FGL Catalog \(\gamma\)-ray sources using the Green Bank Telescope at 350 MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data; 10 of these were discoveries unique to our survey. Sixteen are binaries, with eight having short orbital periods \(P_B < 1\) day. No radio pulsations from young pulsars were detected, although three targets are coincident with apparently radio-quiet \(\gamma\)-ray pulsars discovered in LAT data. Here, we give an overview of the survey and present radio and \(\gamma\)-ray timing results for the 10 MSPs discovered. These include the only isolated MSP discovered in our survey and six short-\(P_B\) binary MSPs. Of these, three have very low-mass companions (\(M_c\) \(\ll\) 0.1M\(_{\odot}\)) and hence belong to the class of black widow pulsars. Two have more massive, non-degenerate companions with extensive radio eclipses and orbitally modulated X-ray emission consistent with the redback class. Significant \(\gamma\)-ray pulsations have been detected from nine of the discoveries. This survey and similar efforts suggest that the majority of Galactic \(\gamma\)-ray sources at high Galactic latitudes are either MSPs or relatively nearby non-recycled pulsars, with the latter having on average a much smaller radio/\(\gamma\)-ray beaming ratio as compared to MSPs. It also confirms that past surveys suffered from an observational bias against finding short-\(P_B\) MSP systems.