We give a description of the design, construction and testing of the 30 and 44 GHz Front End Modules (FEMs) for the Low Frequency Instrument (LFI) of the Planck mission to be launched in 2009. The scientific requirements of the mission determine the performance parameters to be met by the FEMs, including their linear polarization characteristics. The FEM design is that of a differential pseudo-correlation radiometer in which the signal from the sky is compared with a 4-K blackbody load. The Low Noise Amplifier (LNA) at the heart of the FEM is based on indium phosphide High Electron Mobility Transistors (HEMTs). The radiometer incorporates a novel phase-switch design which gives excellent amplitude and phase match across the band. The noise temperature requirements are met within the measurement errors at the two frequencies. For the most sensitive LNAs, the noise temperature at the band centre is 3 and 5 times the quantum limit at 30 and 44 GHz respectively. For some of the FEMs, the noise temperature is still falling as the ambient temperature is reduced to 20 K. Stability tests of the FEMs, including a measurement of the 1/f knee frequency, also meet mission requirements. The 30 and 44 GHz FEMs have met or bettered the mission requirements in all critical aspects. The most sensitive LNAs have reached new limits of noise temperature for HEMTs at their band centres. The FEMs have well-defined linear polarization characteristcs. © 2009 IOP Publishing Ltd and SISSA.