Structural and magnetic properties of Fe thin films grown epitaxially on Rh(001) are studied by spin- and angle-resolved valence-band photoemission, Fe 2p3/2 photoelectron diffraction, and x-ray magnetic circular dichroism experiments. The valence-band structure shows characteristic features of a fcc high-spin state at 4 monolayers (ML) and those of ferromagnetic bulk bcc Fe at 8 ML. The structure of the Fe film reveals fct(001) compressed along the direction perpendicular to the surface in the low-coverage region and gradually changes to distorted bcc(110) as the film thickness increases. The magnetic moments increase as a function of the film thickness and reach the same value as in bulk bcc Fe above 6 ML. The Fe films show in-plane ferromagnetism above 2 ML, and the thickness dependence of the magnetic properties is discussed in connection with the characteristic growth mode.