A longitudinal magnetic field with a strength of 5.2 kG was recently detected in CPD -62 degrees 2124, which has a fractional main-sequence lifetime of about 60 per cent. Strongly magnetic early-B type chemically peculiar stars in an advanced evolutionary state are of special interest to understand the evolution of the angular momentum and spin-down time-scales in the presence of a global magnetic field. We made use of 17 FORS 2 low-resolution spectropolarimetric observations and 844 ASAS3 photometric measurements for the determination of the rotation period, pulsationsand the magnetic field geometry of the star. We calculated periodograms and applied phenomenological models of photometric, spectral and spectropolarimetric variability. We found that all quantities studied, specifically equivalent widths, the mean longitudinal magnetic field <B-z > and the flux in the V filter, vary with the same period P = 2.628 d, which was identified as the rotation period. The observed variations can be fully explained by a rigidly rotating main-sequence star with an uneven distribution of chemical elements, photometric spots and a stable, nearly dipolar magnetic field with a polar field strength of about 21 kG, frozen into the body of the star. The magnetic field of CPD -62 degrees 2124 is tilted to the rotation axis by beta = 28 degrees +/- 7 degrees, while the inclination of the rotation axis towards the line of sight is only i = 20 degrees +/- 5 degrees. In the acquired FORS 2 spectra, we detect short-term line profile variations indicating the presence of beta Cephei type pulsations. As of today, no other pulsating star of this type is known to possess such a strong magnetic field.