The concept of a magnetic tunnel junction (MTJ) fabricated on an active substrate made of a highly magnetostrictive ferromagnetic material is described theoretically. It is shown that, under certain conditions, such hybrid device exhibits strongly enhanced sensitivity of the tunnel current to the external magnetic field. This feature results from the field-induced substrate deformations, which create lattice strains in the MTJ due to the interfacial mechanical interaction. If the free electrode of MTJ is made of a cubic ferromagnet like Co40Fe60 having strong magnetoelastic coupling between the magnetization and strains, the field-induced magnetization reorientation here may be enhanced by the strain effect drastically. This reorientation should lead to a change in the junction's electrical conductance because the magnetization of the reference electrode may be pinned by adjacent antiferromagnetic layer to keep its initial direction. Taking into account additional strain effects on the height and width of the tunnel barrier and the effective mass of tunneling electrons, we performed numerical calculations of the conductance magnetosensitivity for the CoFe/MgO/CoFeB junctions mechanically coupled to the FeGaB film grown on Si and found that such hybrid device is promising as an ultrasensitive room-temperature magnetic-field sensor. Published by AIP Publishing.