The magnetoelectric effect is a key issue for material science and is particularly significant in the high frequency band, where it is indispensable in industrial applications. Here, we present for the first time, a study of the high frequency tunneling magneto-dielectric (TMD) effect in nanogranular FeCo-MgF films, consisting of nanometer-sized magnetic FeCo granules dispersed in an MgF insulator matrix. Dielectric relaxation and the TMD effect are confirmed at frequencies over 10 MHz. The frequency dependence of dielectric relaxation is described by the Debye-Fröhlich model, taking relaxation time dispersion into account, which reflects variations in the nature of the microstructure, such as granule size, and the inter-spacing between the granules that affect the dielectric response. The TMD effect reaches a maximum at a frequency that is equivalent to the inverse of the relaxation time. The frequency where the peak TMD effect is observed varies between 12 MHz and 220 MHz, depending on the concentration of magnetic metal in the nanogranular films. The inter-spacing of the films decreases with increasing magnetic metal concentration, in accordance with the relaxation time. These results indicate that dielectric relaxation is controlled by changing the nanostructure, using the deposition conditions. A prospective application of these nanogranular films is in tunable impedance devices for next-generation mobile communication systems, at frequencies over 1 GHz, where capacitance is controlled using the applied magnetic field.