The PreProcessor of the ATLAS Level-1 Calorimeter Trigger prepares the analogue trigger signals sent from the ATLAS calorimeters by digitising, synchronising, and calibrating them to reconstruct transverse energy deposits, which are then used in further processing to identify event features. During the first long shutdown of the LHC from 2013 to 2014, the central components of the PreProcessor, the Multichip Modules, were replaced by upgraded versions that feature modern ADC and FPGA technology to ensure optimal performance in the high pile-up environment of LHC Run 2. This paper describes the features of the new Multichip Modules along with the improvements to the signal processing achieved.