In tetragonally distorted Fe_1−xCo_x alloy films grown epitaxially on Pd(001), Ir(001), and Rh(001) substrates, a strong uniaxial anisotropy and an easy-magnetization axis perpendicular to the film plane are observed. The strongest perpendicular anisotropy is achieved when the Fe_0.5Co_0.5 films are grown on Rh(001) (c/a=1.24) and it systematically decreases for Ir(001) (c/a=1.18) and Pd(001) (c/a=1.13) substrates in agreement with the theoretical predictions. For the Fe_1−xCo_x films grown on Rh(001) the easy-magnetization axis remains perpendicular up to 15 ML in a broad composition range even at room temperature, which is different from the Fe_1−xCo_x films grown on Pd(001) showing a perpendicular easy-magnetization axis only for x=0.5 and only at low temperature. By growing a pseudomorphic buffer layer of Pd on Rh(001) it is shown that the substrate lattice constant and the resulting film distortion are the factors which are decisive for the uniaxial magnetic anisotropy of the Fe_1−xCo_x films of the same composition.