In the present study, laser wakefield acceleration of electrons in a magnetically controlled plasma was investigated. The results indicated that by employing a linearly chirped laser pulse propagating through magnetized plasma with a reversed external magnetic field, higher energy electrons are obtained compared to unmagnetized plasma and/or non-chirped laser pulse. Besides, by considering an appropriate chirping constant magnitude and an axial external magnetic field, one could obtain remarkable GeV electron energies. It was also found that the effect of external magnetic field direction on the electron energy is not sensed much in the mildly relativistic regime, while the reversed magnetic field increases the peak of electron energy gains compared with the forward magnetic field in the highly relativistic regime. For the mildly relativistic case, peak energy of 412 MeV and relative energy spread of 7% was obtained. In addition, for high relativistic case, peak energy of 1.55 GeV was obtained.