We present a simple, low-cost, and environmental-friendly method for the fabrication of hybrid magnetorheological composites (hMCs) based on cotton fibers soaked with a mixture of silicone oil (SO), carbonyl iron (CI) microparticles, and iron oxide microfibers (μF). The obtained hMCs, with various ratios (Φ) of SO and μF, are used as dielectric materials for manufacturing electrical devices. The equivalent electrical capacitance and resistance are investigated in the presence of an external magnetic field, with flux density B. Based on the recorded data, we obtain the variation of the relative dielectric constant (ϵr′), and electrical conductivity (σ), with Φ, and B. We show that, by increasing Φ, the distance between CI magnetic dipoles increases, and this leads to significant changes in the behaviour of ϵr′ and σ in a magnetic field. The results are explained by developing a theoretical model that is based on the dipolar approximation. They indicate that the obtained hMCs can be used in the fabrication of magneto-active fibers for fabrication of electric/magnetic field sensors and transducers.