This paper investigates the possibilities of creating magnetic field sensors using the direct magnetoelectric (ME) effect in a monolithic heterostructure of amorphous ferromagnetic material/langatate. Layers of 1.5 μm-thick FeCoSiB amorphous ferromagnetic material were deposited on the surface of the langatate single crystal using magnetron sputtering. At the resonance frequency of the structure, 107 kHz, the ME coefficient of linear conversion of 76.6 V/(Oe∙cm) was obtained. Furthermore, the nonlinear ME effect of voltage harmonic generation was observed with an increasing excitation magnetic field. The efficiency of generating the second and third harmonics was about 6.3 V/(Oe2∙cm) and 1.8 V/(Oe3∙cm), respectively. A hysteresis dependence of ME voltage on a permanent magnetic field was observed due to the presence of α-Fe iron crystalline phases in the magnetic layer. At the resonance frequency, the monolithic heterostructure had a sensitivity to the AC magnetic field of 4.6 V/Oe, a minimum detectable magnetic field of ~70 pT, and a low level of magnetic noise of 0.36 pT/Hz1/2, which allows it to be used in ME magnetic field sensors.