Co-rich Co-Pt films (thickness 5 - 1000 nm) were electrodeposited under galvanostatic conditions onto (0001)-oriented ruthenium seed layers. The films grow mainly with a hexagonal close packed structure, with the c axis oriented perpendicular to the film plane The growth occurs epitaxially on top of the Ru seed, and thin films reproduce the grain size and morphology of the seed layer. Thick films grow with a columnar microstructure; the extent of coarsening of the column diameter depends on the growth rate and becomes negligible for current densities above 50 mA/cm2. The films exhibit a perpendicular magnetic anisotropy, and the magnetic properties depend on thickness and growth rate. Films grown at low rate present lower coercivity; the high coercivity observed in films grown at high rate is attributed to the formation of defects during growth. At large thickness, the magnetic properties are dominated by the demagnetizing fields. copyright The Electrochemical Society.