We report on the design and the construction of a sounding rocket payload capable of performing atom interferometry with Bose-Einstein condensates of 41 K and 87 Rb. The apparatus is designed to be launched in two consecutive missions with a VSB-30 sounding rocket and is qualified to withstand the expected vibrational loads of 1.8 g root-mean-square in a frequency range between 20–2000 Hz and the expected static loads during ascent and re-entry of 25 g. We present a modular design of the scientific payload comprising a physics package, a laser system, an electronics system and a battery module. A dedicated on-board software provides a largely automated process of predefined experiments. To operate the payload safely in laboratory and flight mode, a thermal control system and ground support equipment has been implemented and will be presented. The payload presented here represents a cornerstone for future applications of matter wave interferometry with ultracold atoms on satellites.