Circular conducting waveguides filled with gyroelectric media are studied in this paper and the dyadic Green's functions in these waveguides are obtained for the first time. The electric and magnetic fields in the waveguide are expressed in terms of cylindrical vector wave function expansion. It is shown that each of the eigenmodes in the waveguide consists of two eigenwaves whose wave numbers can be determined by the characteristic equation. Dispersion relation is obtained by applying boundary conditions to the eigenmodes. Mode orthogonality is discussed before the orthogonal relations are formulated and then used to determine the expansion coefficients of electric and magnetic fields. The complete expansions of both the electric and the magnetic dyadic Green's functions are finally obtained. The calculated dispersion curves are depicted and discussed while effects of gyrotropy are shown.