Born in Oslo, Peters studied drawing from 1867 to 1870 under David Arnesen and J.F. Eckersberg. Working as an illustrator, he came to the attention of Karl IV who made arrangements for him to study at the Royal Swedish Academy in Stockholm from 1871 to 1873. He then went to Rome where he studied under Antonio Piccinni from 1873 to 1876, completing his studies in 1880 after periods in Munich and Paris."Wilhelm Peters", Storre norske leksikon. Retrieved 17 October 2013.Elisabeth Fabritius, "Wilhelm Peters", Kunstindeks Danmark & Weilbachs Kunstnerleksikon. Retrieved 18 October 2013.
