We electrodeposited ultrathin magnetic Fe and Co films on Cu(001) crystals from an aqueous 0.3 M Na₂SO₄/(Fe or Co)SO₄ electrolyte in a newly developed electrochemical cell. A deposition procedure of Fe from an organic electrolyte of propylene carbonate has been additionally developed to prevent the significant H₂ evolution during the Fe deposition from an aqueous electrolyte. Fe films of more than 8 monolayer (ML) thickness show the easy magnetization axis in plane. The saturation magnetization correlates linearly with the film thickness. In the thickness range between 2 and 8 ML, the easy magnetization axis is in the [001] direction. No magnetization is observed in films with thickness of less than 2 ML. Co films show in-plane magnetization with square hysteresis loops and a linear correlation of the saturation magnetization and film thickness above 2 ML. The magnetization vanishes at coverages of less than 1.5 ML as known from molecular beam epitaxy grown films. The coercive field of the Co films varies approximately linearly from 0.9 mT at 2.5 ML to 25 mT at 51 ML film thickness.