The DAMPE (DArk Matter Particle Explorer) is a scientific satellite being developed in China, aimed at cosmic ray study, gamma ray astronomy, and searching for the clue of dark matter particles, with a planned mission period of more than 3 years and an orbit altitude of about 500 km. The BGO Calorimeter, which consists of 308 BGO (Bismuth Germanate Oxid) crystal bars, 616 PMTs (photomultiplier tubes) and 1848 dynode signals, has approximately 32 radiation lengths. It is a crucial sub-detector of the DAMPE payload, with the functions of precisely measuring the energy of cosmic particles from 5 GeV to 10TeV, distinguishing positrons/electrons and gamma rays from hadron background, and providing trigger information for the whole DAMPE payload. The dynamic range for a single BGO crystal is about 2?105 and there are 1848 detector signals in total. To build such an instrument in space, the major design challenges for the readout electronics come from the large dynamic range, the high integrity inside the very compact structure, the strict power supply budget and the long term reliability to survive the hush environment during launch and in orbit. Currently the DAMPE mission is in the end of QM (Qualification Model) stage. This paper presents a detailed description of the readout electronics for the BGO calorimeter.