It is well known that massive O stars are frequently (if not always) found in binary or higher-order multiple systems, but this fact has been less robustly investigated for the lower mass range of the massive stars, represented by B-type stars. Obtaining the binary fraction and orbital parameter distributions of B-type stars is crucial to understand the impact of multiplicity on the archetypal progenitor of core-collapse supernovae as well as to properly investigate formation channels for gravitational wave progenitors. This work aims to characterise the multiplicity of the B star population of the young open cluster NGC 6231 through multi-epoch optical spectroscopy of 80 B-type stars. We analyse 31 FLAMES/GIRAFFE observations of 80 B-type stars, monitoring their radial velocities (RVs) and performing a least-squares spectral analysis (Lomb-Scargle) to search for periodicity in those stars with statistically significant variability in their RVs. We constrained an observed spectroscopic binary fraction of 33+/-5% for the B-type stars of NGC 6231, with a first order bias correction giving a true spectroscopic binary fraction of 52+/-8%. Out of 27 B-type binary candidates, we obtained orbital solutions for 20 systems: 15 single-lined (SB1) and five double-lined spectroscopic binaries (SB2s). We present these orbital solutions and the orbital parameter distributions associated with them. Our results indicate that Galactic B-type stars are less frequently found in binary systems than their more massive O-type counterparts, but their orbital properties generally resemble those of B- and O-type stars in both the Galaxy and Large Magellanic Cloud.