The work is devoted theoretical and experimental studies of a magnetoelectric gyrator, consisting of an inductor coil, inside which there is a magnetoelectric heterostructure, which is a mechanically connected piezoelectric layer and two magnetic layers. Using the system of equations of elasto- and electrodynamics for the piezoelectric and magnetostrictive phases, expressions are obtained for the current/voltage conversion coefficient of the gyrator in terms of the phase parameters of the heterostructure. An experimental sample of a gyrator based on the Metglas/PZT/Metglas heterostructure was fabricated. Theoretically calculated and experimentally studied the frequency and load characteristics of the gyrator. It is shown that theoretical calculations are in good agreement with experimental data. Recommendations for the creation of gyrators with the highest current/voltage conversion efficiency are presented.