Wilhelm Christophersen was born at Brevik in Telemark, Norway. The son of a customs official in the town, he was a brother of Christian Christophersen and Peter Christophersen and the grand-uncle of Erling Christophersen. In June 1876, he married Swedish citizen Berta Alexandra Juliane Carola Juhlin-Dannfelt (1856–1943).
He earned his examen artium in 1850. After a brief career as a private tutor in the Netherlands, Christophersen entered the study of law at the Royal Frederick University (now the University of Oslo) in 1853, graduating in 1857. He worked as a language teacher to finance his education.
From 1857 he worked in the Ministry of Auditing, but in 1859 his language skills got him an assignment within the Ministry of the Interior's office for trade and consular affairs. In 1864 he was transferred to the Swedish-Norwegian foreign service. He served as consul in Barcelona from 1864 and in Buenos Aires from 1868 to 1870, and then as consul-general in the same city until 1878. Having secured this position, he was stationed in Paris; Leith, Scotland; and Antwerp. Upon the dissolution of the union between Norway and Sweden in 1905, he stayed in Antwerp in the same position, only for the Norwegian government.
As a professional within the field of Swedish-Norwegian foreign affairs, Christophersen's career was limited by his lack of family connections and financial resources. As he had served on the commission to study a separate consular corps for Norway, as well as other committees on the topic, he fell out of Oscar II's good graces. As consul, he had several notable accomplishments:
As foreign minister, his in-depth knowledge and field experience with consular affairs made him particularly suited to build a foreign service organization to serve Norwegian economic interests. He also worked to reconcile relations between Norway and Sweden. His wife was Swedish, the daughter of a Swedish diplomat. He accepted the position as foreign minister on the condition that he was able to return to his post as consul general in Antwerp. But he instead was awarded an adequate pension and remained in Norway.