Only a small fraction of massive stars seem to host a measurable structured magnetic field, whose origin is still unknown and whose implications for stellar evolution still need to be assessed. Within the context of the "B fields in OB stars (BOB)" collaboration, we used the HARPSpol spectropolarimeter to observe the early B-type stars β CMa (HD 44743; B1 II/III) and ɛ CMa (HD 52089; B1.5II) in December 2013 and April 2014. For both stars, we consistently detected the signature of a weak (<30 G in absolute value) longitudinal magnetic field, approximately constant with time. We determined the physical parameters of both stars and characterise their X-ray spectrum. For the β Cep star β CMa, our mode identification analysis led to determining a rotation period of 13.6 ± 1.2 days and of an inclination angle of the rotation axis of 57.6 ± 1.7°, with respect to the line of sight. On the basis of these measurements and assuming a dipolar field geometry, we derived a best fitting obliquity of about 22° and a dipolar magnetic field strength (Bd) of about 100 G (60