We present the first Fermi Large Area Telescope (LAT) catalog of long-term gamma-ray transient sources (1FLT). This comprises sources that were detected on monthly time intervals during the first decade of Fermi-LAT operations. The monthly timescale allows us to identify transient and variable sources that were not yet reported in other Fermi-LAT catalogs. The monthly data sets were analyzed using a wavelet-based source detection algorithm that provided the candidate new transient sources. The search was limited to the extragalactic regions of the sky to avoid the dominance of the Galactic diffuse emission at low Galactic latitudes. The transient candidates were then analyzed using the standard Fermi-LAT maximum likelihood analysis method. All sources detected with a statistical significance above 4 sigma in at least one monthly bin were listed in the final catalog. The 1FLT catalog contains 142 transient gamma-ray sources that are not included in the 4FGL-DR2 catalog. Many of these sources (102) have been confidently associated with active galactic nuclei (AGNs): 24 are associated with flat-spectrum radio quasars, 1 with a BL Lac object, 70 with blazars of uncertain type, 3 with radio galaxies, 1 with a compact steep-spectrum radio source, 1 with a steep-spectrum radio quasar, and 2 with AGNs of other types. The remaining 40 sources have no candidate counterparts at other wavelengths. The median gamma-ray spectral index of the 1FLT-AGN sources is softer than that reported in the latest Fermi-LAT AGN general catalog. This result is consistent with the hypothesis that detection of the softest gamma-ray emitters is less efficient when the data are integrated over year-long intervals.