White dwarf stars are the most common stellar fossils. When in binaries, they make up the dominant form of compact object binary within the Galaxy and can offer insight into different aspects of binary formation and evolution. One of the most remarkable white dwarf binary systems identified to date is AR Scorpii (AR Sco). AR Sco is composed of an M dwarf star and a rapidly spinning white dwarf in a 3.56 h orbit. It shows pulsed emission with a period of 1.97 min over a broad range of wavelengths, which led to it being known as a white dwarf pulsar. Both the pulse mechanism and the evolutionary origin of AR Sco provide challenges to theoretical models. Here we report the discovery of a sibling of AR Sco, J191213.72-441045.1, which harbours a white dwarf in a 4.03 h orbit with an M dwarf and exhibits pulsed emission with a period of 5.30 min. This discovery establishes binary white dwarf pulsars as a class and provides support for proposed formation models for white dwarf pulsars.