This paper describes the design, construction, and performance of the wideband orthomode transducers (OMTs) for the L- (1.2-1.8 GHz), the S- (2-3 GHz) and the P- (0.56-1.12 GHz) band receiver systems of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). These OMTs operate at the cryogenic temperature of 70K to reduce their thermal noise contribution to the receiver chains. The development on the FAST L- and S-band quad-ridged waveguide (QRWG) OMTs is carried out based on the theoretical mode analysis. In view of the miniaturization of FAST cryogenic receiver system at P-band, a novel wideband compact bowtie dipole OMT is designed with an octave bandwidth as well as a length of only quarter wavelength. The proposed L-, S- and P-band OMTs are designed and optimized by using Ansys High Frequency Structure Simulator (HFSS), and then manufactured, tested at room temperature. Measurement of FAST cryogenic receiver system noise is also performed with the L-, S- and P-band OMTs installed. The measured results fully comply with the design specifications.