Astrometric monitoring of the nearby early-L dwarf DE0823$-$49 has revealed a low-mass companion in a 248-day orbit that was announced in an earlier work. Here, we present new astrometric and spectroscopic observations that allow us to characterise the system in detail. The optical spectrum shows LiI-absorption indicative of a young age and/or substellar mass for the primary component. The near-infrared spectrum is best reproduced by a binary system of brown dwarfs with spectral types of L1.5 $+$ L5.5 and effective temperatures of $2150pm100$ K and $1670pm140$ K. To conform with the photocentric orbit size measured with astrometry and the current understanding of substellar evolution, the system must have an age in the 80--500 Myr range. Evolutionary models predict component masses in the ranges of $M_1simeq0.028-0.063,M_odot$ and $M_2simeq0.018-0.045,M_odot$ with a mass ratio of $qsimeq0.64-0.74$. Multi-epoch radial velocity measurements unambiguously establish the three-dimensional orbit of the system and allow us to investigate its kinematic properties. DE0823$-$49 emerges as a rare example of a nearby brown dwarf binary with orbit, component properties, and age that are characterised well. It is a juvenile resident of the solar neighbourhood, but does not appear to belong to a known young association or moving group.
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