A scanning tunneling microscopy (STM) study is presented of the growth of Ni films on Cu(100). From a series of STM images taken of the same surface region during film growth, detailed information is gained on the film growth and morphology. Multilayer growth starts after nearly layer-by-layer growth of 3.5 layers, and becomes dominant above film thicknesses of 6 ML. Above 4 ML the islands are of rectangular shape, with their edges along [011] and [01-bar1] directions. Annealing the film at a temperature of 450 K smooths the film surface without any significant substrate interdiffusion. Magneto-optical Kerr-effect measurements show the magnetization of a 10.2-ML film to remain perpendicular with a reduction less than 15% in amplitude, suggesting that the morphology is not responsible for the spin reorientation in this system.