The contributions of the vector and scalar components to the magnetically dependent microwave transition frequency light shift are analyzed and the compensation of these components is experimentally demonstrated for the 87Rb atoms optically oriented by a laser tuned to the D 2 line of the head doublet. The Allan variance is studied as a function of the averaging time for a tandem of optically pumped quantum magnetometers (OPQMs), one of which is based on a low-frequency spin oscillator while another is based on a quantum microwave discriminator with a resonance frequency that corresponds to magnetically dependent transitions between HFS sublevels with the extremal value of the magnetic quantum number. It is shown that the compensation of the scalar and vector components of the light shift in OPQMs reduces the Allan variance at averaging times that exceed hundreds of seconds compared to a quantum discriminator based on the magnetically independent 0–0 transition. In this case, the minimal Allan variance in OPQMs at the end resonance is achieved at considerably longer averaging times than in the case of the quantum discriminator that is tuned to the 0–0 transition frequency.